Potential of the single-screw compressor *

G. G. Haselden

Keywords: compressor , ga te ro to r design

Les possibilit6s du compresseur monovis Le compresseur monovis pourrait devenir /e type dominant de compresseur pour des puissances de 50 ~ 1500 kW. I/est susceptible d'un rendement #nerg~tique ~/ev~ parce que /es

pertes dues aux fuiteS, au frottement et aux transferts de chaleur pourraient #tre fortement r#duites. On d#crit ~ cet effet un nouveau type de satellite. On peut obtenir un coot peu #lev6 parce que lecompresseur est de faible encombrement, que le nouveau satellite est de fabrication moins co,reuse, que les paliers peuvent #tre simplifies et que le corps peut devenir un simple r#servoir sous pression.

The single-screw compressor has the potential to become the dominant form of compressor in the 50 -150kW power range. It is capable of high energy efficiency because losses due to leakage, frictional effects and heat transfer factors are capable of being reduced to a low

level. A new gaterotor design for this purpose is described. Low cost is possible because the compressor is compact, the new gaterotor is less expensive to manufacture, the bearings can be simplified, and the casing can become a simple pressure vessel.

The past twenty years have seen the Lysholm twin- screw compressor progressively penetrate the medium power (say 50-1 500 KW) range of duties, especially for vapour compression. I believe that the Zimmern single-screw compressor has the potential to replace it in the next 20 years.

Both forms of screw compressor share the advan- tages of:

1. dynamical ly balanced components, allowing speeds of rotation which match those of the cheapest motors, and producing low wear; 2. el imination o f valves, giving high reliability and reducing losses; 3. compactness, so that the compressor is generally smaller than the driver; 4. eff icient unloading, giving step-less throughput reduction and low-load starting.

The technical factors which favour single-screw geo- metry comprise the'following: (1) improved perfor- mance, due to reductions of leakage losses, frictional losses, and heat transfer effects; (2)/owercost, due to savings in the manufacturing costs of rotors, casing, including the unloading gear, and bearings. The re- mainder of the Paper will explore the scope of each of the above items.

Leakage losses

In screw compressors leakage through the positive clearances between the rotors, and between each rotor

The author is from the Department of Chemical Engineering. The University of Leeds. Leeds LS29JT, U K. Paper received 1 April 1985. * Text of a lecture given on 12 January 1985 at Trondheim, Norway, at an international meeting to honour the 70th birthday of Professor Gustav Lorentzen.

and the casing, is the largest factor governing both the volumetric and isentropic efficiencies. For the single- screw machine the leakage situation has been analysed by Chan et al. 1

The leakage paths are defined in Fig. 1. L1 and L2 are the leakage paths between the main rotor and the cylindrical casing, over the dividing walls between the flutes. The former is always shorter than the latter, but the relative flow rates differ depending on rotational position. In general the L1 leakage is trapped by the following flute so it affects only the energy efficiency not the volumetric efficiency. L3 is the lip clearance between the face of the gaterotor tooth and the slit opening in the casing through which it protrudes. Leakage by this path goes into the gate rotor housing which is in direct communication with suction. L4 defines the leakage around the two sides and end of the engaged tooth. The total length of this leakage path varies greatly with rotor angle, being already large at the point of seal, rising quickly to a flat maximum and then diminishing to zero. The back of the tooth always communicates with suction. The remaining leakage path, L5. is from the end of the flute through the radial clearance between the delivery end of the main rotor and the casing, and into the end housing which communicates with suction.

The different leakage paths have very different geometries, they also have different amounts of relative movement between the leakage surfaces, nevertheless the flow through them can be calculated with an accuracy of ~ ___20%. The calculated leakage flows for a dry vapour situation with a typical compressor running on R22 are presented in Fig. 2. The area under each curve represents the total leakage for a single stroke, and the curve LK gives the algebraic sum of all the leakages. Numerically L2 causes the largest lea- kage, but the super-charging effect of L1 is such that

0140-7007/85/04021 5-06S 3.00 © 1985 Butterworth 8 Co (Publishers) Ltd and IIR Volume 8 Num6ro 4 Juillet 1985 215

I '

Fig. 1 Designation of the leakage paths in the single-screw compressor

F1~7. 1 Localisation des fuites dans le compresseur monovis

2 0

15

o ~ r lO

o

IE

. . . . . . . L I !

............... L 2 / " ~ . . ______ L3 .. ...

I \ . . . . . . L4 • . . . . . . . . . . . 1_5

/ " ~ .... 1-6 / ~ . . . . . . . . L K . / -,.

\

............ 2/: ...... . ........

_ 1 / / I - - . .....

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- 1 0 I I I I , I I I I 0 2 0 4 0 6 0 8 0 100 120 140 160 180

ROTOR A N G L E DEGREE

Fig. 2 Mass leakage rates calculated for a single f lute of a compressor running on R22 at 2950 r.p.m., on a - 5 / + 35°C duty. the VR being 2.6, and the clearances 0 . 1 0 m m

Fig. 2 Taux de fuite massique calculus pour une seule rainure de eompresseur fonctionnant au R 22 b 2950 t/rain, ~ des temperatures de - 5 / + 35~C, /e proportion de volume #tant de 2,6 et /e jeu de O, lOmm

overall leakage is negative for the first 30 °. Thus, L1 and L2 off-set each other to a considerable extent, and so have a relatively small effect on volumetric efficiency, though their effect on energy consumption is larger. The main contr ibution to loss of volumetric efficiency is leakage around the gaterotor tooth, and it has a corresponding effect on power consumption.

For the specified duty, assuming perfect operation apart from leakage through uniform clearances of

0.1 mm, the calculated values of the volumetric and isentropic efficiencies are 94 and 89.5%, respectively, and for clearances of 0.05 mm they are 96.5 and 93.5%. When these values are compared with the measured performance of oi l- lubricated machines two points emerge. Firstly, with the single-screw compressor it is unnecessary to have oil present to achieve acceptable levels of leakage. The volumetric efficiencies achieved with oil are no better than those expected in a dry compression situation. Secondly, since the achieved isentropic efficiencies are not much > 70%, the pre- sence of oil must produce large churning and other frictional losses which result in signif icant power wastage.

In vapour compression there is much to be said for eliminating oil and using the liquid phase of the compressed vapour as the sealant and coolant 2. Not only can this approach simplify a refrigeration or heat pump cycle but in some cases it can make them thermodynamically more efficient. A crucial factor, however, is leakage since liquid leakage is potentially much more serious than gas leakage, due not only to its greater density but to its susceptibil ity to relative surface movement.

Tests have shown 3 that the effect of relative surface movement on f low through small clearances is generally negligible for gas but can be dominant for l iquid leakage. For instance with a 280mm single- screw compressor running at 2950 r.p.m, the maximum surface speed is <25% of the sonic velocity for R22 under operating conditions. Since most vapour lea- kage occurs under choked f low condit ions the effect of rotor movement on the calculated vapour leakage loss is small, and this was confirmed experimentally. By contrast, when the liquid phase is present, surface movement at the prevailing speed can dominate the leakage situation. For instance, if the movement is in- line with leakage direction it can drag liquid through the clearance and produce effective leakage even in the absence of a pressure driving force, whi lst motion opposed to the leakage direction can bring liquid leakage to zero although the prevailing pressure differ- ence is 10bar*.

Fig. 3 shows the calculated rate of l iquid leakage, al lowing for surface movement, under the same con- ditions as for Fig. 2 assuming that liquid R22 was injected at a sufficient rate to fill all the leakage paths but wi thout producing significant l iquid ho ld -up

The overall pattern of leakage is seen to be similar but the absolute rate is increased by a factor of ~7, which would lead to a whol ly unacceptable volumetric efficiency. Also, L2 (leakage between the main rota and casing) develops much more rapidly and is off-set less by L1.

In fact, the effect of l iquid leakage on the probable volumetric and isentropic efficiencies is a good deal more complex than is indicated by Fig. 3. Only if the liquid is totally evaporated after leakage does it equate to vapour leakage. If, by contrast, it undergoes isen- thalpic flashing, and the remaining liquid drains away at low pressure, then only ~10% of the leakage represents true loss. In fact it is not easy to provide for this flashed liquid to drain to the evaporator, and much

* 1 b a r = l O 0 kPa

216 International Journal of Refrigeration

15(~

10C

Q

. J

~ o

I [

- I O C

. . . . . 1.1

. . . . . . . . . . . L 2

L 3

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/ . : i . . . . . . . . . . . . \ _ . . . . . L ,

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11

20 ,~ & 4 ' ,~o ,;o ,4o 40 ,8o R O T O R A N G L E D E G R E E

Fig. 3 .Corresponding leakage rates for liquid R22 for the same compressor and duty

Fig. 3 Taux de fuire correspondants pour/e R22 liquide pour le re&me compresseur et /es re&rues tempOratures

of it is likely to evaporate due to internal heat transfer within the compressor. It is necessary to consider separately the fate of the flashed liquid for each of the leakage paths.

The L1/L2 leaked liquid, having flashed, is likely to continue flowing as a film along the inner wall of the casing towards suction. Because the film is very thin it will soon be brought to rest by viscous forces causing the film to thicken. Within an interval of ~O.003s, however, the next flute wall will pass over it and will plough the liquid in the reverse direction towards delivery. This ploughing action will lead to a balance between the mechanical forces pushing the liquid towards delivery, and a pressure force pushing it towards suction. The pressure force diminishes to zero as the suction seal point is approached, hence there is no driving force to cause rejection of flashed liquid at the suction end of the machine. Forth is reason much of the injected liquid must accumulate within the flutes, undergoing multiple flashes, until it is ploughed out at the delivery end.

The liquid which leaks around the tooth will probably suffer a similar fate. The flashed liquid will continue to flow as a film on the flute walls but centrifugal force will cause it to gravitate to the outer edge of the main rotor and hence onto the casing wall. The worst situation will arise with the liquid leakage, L5, over the end of the flute and into the low pressure cavity at the delivery end of the main rotor. Here centrifugal force will prevent it from draining away, and it is likely to accumulate until the surface area available for heat transfer is sufficient to evaporate it, the heat being supplied by condensation of product vapour.

These considerations indicate that the potential advantages of oil-free liquid-injected operation can be realized only if leakage losses can be substantially reduced. Measures to do this will be presented.

Frict ional losses

Performance measurements on oil-injected single- screw compressors indicate that at least 10% of shaft

work is consumed as friction due to churning and bearing losses. The bearing losses can be expected to be much lower with the single-screw compressor because very much lighter units may be employed. Churning losses will be associated almost wholly with the main rotor. It is desirable to keep the flute walls as thin as possible, and to minimize the length of the cylindrical sealing section at the delivery end. In some versions of the machine this surface is grooved to form a labyrinth. A much better solution would be to eliminate most of this cylindrical surface and to use instead a sprung lip seal bearing against the discharge end of the rotor, near to its outer diameter.

Heat t ransfer e f fec ts

Particularly in the case of oil-free liquid-injected oper- ation heat transfer effects within the compressor can become very serious. Hints have already been given in relation to the flute end leakage at the discharge end of the compressor. Here the high heat transfer coefficient associated with condensation will cause all the com- pressor surfaces in contact with discharge to be at near-saturation temperature. However, any liquid lea- ked into the rotor end cavity will be at suction pressure and temperature, in a situation in which the surface heat transfer coefficient will also be high. Hence, unless thermal insulation is judiciously inserted there will be rapid heat transfer through the small thickness of metal separating the two regions.

In addition there are potentially large heat transfer effects associated with the cyclic temperature profiles to which all the active areas of the rotors and casing are exposed. Thus, for instance, a point on the flute wall near to the discharge end of the main rotor will experience a full pressure and temperature cycle 100 times a second. During suction any liquid on the surface will tend to evaporate, drawing heat from metal below the surface. This effect will continue until the pressure has risen sufficiently for the saturation tem- perature to be above the surface temperature. For the remainder of the compression and discharge parts of the stroke condensation of the compressed vapour will tend to occur, the rate being determined by the thickness of the condensed film and by the thermal diffusivity and the temperature profile of the underlying metal.

Due to the rapidity of the cycle the resulting condensate layerwill be very thin. If it can pass through the gaterotor tooth clearance it will then find itself exposed to suction pressure whilst being in contact with comparatively hot underlying metal. The latter fact will result in a degree of flashing which far exceeds the normal isenthalpic case. Hence, this cyclic temperature effect can lead to performance losses which are similar to leakage effects. Related phenomena occur at points on the inner surface of the casing.

A research student at Leeds (M. Yell) has model- led these effects for R22 on cast iron rotors and casing, and his results indicate that they could account for a 10% power loss. He has also shown that by coating the metal surfaces with a layer of material of low thermal diffusivity, only 0.1 mm thick, the problem could be solved.

Volume 8 Number 4 July 1985 217

Reduction of leakage losses There are several ways in which the clearance between the main rotor and the casing could be reduced but the simplest, probably, is to coat the inner surface of the casing with a relatively soft material which would be abraided by the rotor during an initial running-in period. Since the cylindrical outer surface of the rotor can be easily ground with high precision, and since the main rotor bearings carry a balanced load, it should be possible to sustain radial clearances of 0.02 mm, or even less, for the smallest machines. The main chal- lenge resides with leakage around the gate rotor teeth, especially since the surface motion is most damaging in this location.

With the conventional one-piece plastic star differ- ential contraction/expansion effects are very trouble- some and place severe limits on clearances. Thus, if the compressor is used in refrigeration duties the plastic star, main rotor and casing wil l all cool down to temperatures intermediate between the evaporator and condenser temperatures, though not necessarily by the same amount. In general the areas of each of the com- ponents exposed to low pressure are higher than those exposed to high pressures so there will be a tendency for the average temperature to be nearer the evaporator value. The clearances must be set at room temperature, as this is normally the condition under which it is assembled, and to which it returns when not in use. The expansion (or contraction) coefficient for plastics is 5-10 times that for cast iron, hence under refrigeration conditions the plastic star will contract away from the main rotor and the clearances wil l increase. Conversely for heat pump or process gas compression duties the compressor in operation wil l assume a mean temperature which is above ambient. Therefore, the compressor must be assembled with increased clearances so that under operating con- ditions the star wil l grow differentially to restore the clearances to the desired value.

For example, a 280 mm single-screw compressor assembled at 20°C, with clearances of 0.025 mm, used with an evaporator temperature of -20°C, might be assumed to cool to an average temperature of 0°C. As a result the clearances on the flanks of the tooth will have increased to 0.04 mm whilst that at the end of the tooth wil l have grown to 0.26 mm. The effect of the latter wil l be very great because it occurs during most of the discharge stroke when the pressure difference is max- imum. In heat pump duties the temperature differ- ences will be greater and hence the problems will be increased. Attention has been directed, therefore, to new gaterotor designs which minimize-the differential contraction problem, and also allow for some degree of wear to be taken up.

The tooth~end problem is most readily solved by using separate plastic pads on each tooth and by attaching the pads to the support spider at points near to the ends of the teeth. Solving the flank problem requires an analogue of the piston ring, with sliding elements which can be sprung against the flute wall. A number of ways of achieving a sliding action were considered and the preferred solution is illustrated in Fig. 4. Each insert comprises a large fixed pad which provides the leading edge and is located by integrally cast pegs which are an interference fit in holes in the

)

MAIN ROTOR Fig. 4 New gaterotor design incorporating separate tooth inserts. Arrow indicates direction of rotation

Fig. 4 Nouveau type de satelfite avec dents munies d'une garniture d'#tanch#ir# mobile. La fleche indique /e sens de la rotation

support spider. The larger outer peg provides location and the smaller peg provides alignment. The small sliding pad provides the trailing edge of the preceding tooth and is free to undergo limited circumferential movement sliding under the overlapping fixed pad on the preceding tooth. The fixed pad has a tapered inner section which is designed to act as a stable fulcrum for a spring which holds the moving pad. The spring is constituted by a thin parallel bar of the same material which joins the fulcrum to the sliding pad, its dimen- sions being chosen so that the sliding pad presses against the wall of the main rotor with the required force.

Thus, a one-piece precision moulded insert sho- wed promise of satisfying all the necessary attributes of location, movement and sealing force, provided that the right plastic material was available, and the required dimensions could be achieved. These factors were probed in greater depth. Incidentally, it should be noted that at least two teeth wil l be in engagement with the main rotor at any time, and that the pressure exerted by the moving pads wil l cause a reactive force to push the fixed pads against the main rotor.

A crucial issue is that the sealing pressure pushing the pads against the main rotor should be adequate under all pressure conditions, without being excessive at suction conditions. It should also be to some extent independent of wear. In fact three different sealing forces can be used. Firstly, there is the spring force already described. The limitations which apply are first that the moving pad wil l need to be deflected (even when the tooth is not engaged) by an amount equal to at least five times the required contraction-plus-wear so that during the life of the insert the sealing force is reasonably constant. The spring force would also require to be adequate for the highest delivery pressure.

218 Revue Internationale du Froid

./,I'IF, IN ROTOR FLUTE WALLS

/~/SL|T

~XSUPPORT SPIDER X LOCATION PEG Fig. 5 Section through the fixed and sliding pads

Fig. 5. Section transversale des languettes fixes et coulissantes

The second available force is centrifugal. If a line from the centre of gravity of the sliding pad, passing along the centre-line of the spring, goes through the rotational centre of the gaterotor then the sliding pad will be centrifugally neutral. If the centre of gravity is in advance of that line then on rotation the pad will press against the main rotor with a force dependent on the square of the speed.

The third force is due to fluid pressure exerted in the slit between the fixed and sliding pads, as shown in Fig. 5. The compressed fluid will enter this slit, and since the sliding faces are in close contact and will allow little leakage, it may be assumed that the slit walls, of depth t, ai'e exposed to the prevailing flute pressure. This pressure force will press the sliding pad against the main rotor. Resisting it will be the pressure force exerted by the compressed fluid as it leaks between the pads and the rotor faces, the point of constriction being at a depth x belowthe pad surface. It is to be noted that the line contact between the pads and the flute walls of the main rotor is always designed to be below the pad surface. Under throttling f low conditions the pressure profile in the gap will be one in which the fluid pressure drops to about half the flute pressure at the throat, and then falls off rapidly to suction pressure below the throat. Thus, if t is designed to be a little larger than xthere will always be a nett fluid pressure forcing the moving pad against the moving rotor wall, and this force will automatically adjust itself in proportion to the prevailing flute pressure. The chosen design employs a small spring force to ensure initial engagement, a neutral centrifugal position, and main reliance on fluid pressure in the slit.

Two further issues remain to be settled, whether the sliding pad should be on the leading or trailing edge, and how to restrict its movement to the desired amount. Since the gaterotors are driven by the main rotor the initial thought was that the fixed pad should provide the trailing edge, leaving the moving pad to take up the clearance. A more important consideration arises, however, from the requirements of the sealing pressure. If the pressure in the slit is always to exert a sufficient pressure to ensure a seal then the slit must be near the tailing edge. This is because the maximum pressure in the flute occurs generally after the tooth has

reached the point of maximum insertion, and it con- tinues until the end of discharge. By having the sliding pad as the trailing edge the total force generated by the trailing edges always exceeds the fluid pressure force generated at the leading edges, and the seal will be fully maintained.

The limitation of movement of the sliding pad is necessary otherwise it will be chopped by the main rotor on engagement. The flute wall at entry can be tapered to the extent of say 0.1 mm so as to guide the sliding pad smoothly onto the working face, but the movement of the pad does not want to exceed this amount. The chosen way of limiting the sliding pad movement is just visible in a photograph of a gaterotor spider, with five inserts in position, in Fig. 6. The shaded part of the sliding pad has a hole in it, near to the outer end. A corresponding small peg is cast into the overlapping section of the fixed pad, the difference in diameter of the hole and peg providing the required movement. Since these are incorporated in the mould the control is very precise, and no machining or fitting is involved.

Choice of p last ic

The new design is crtically dependent on the proper- ties of the plastic used to mould the inserts. Happily new composites are now available which are ideal for the duty. The inserts shown in Fig. 6 are moudled in carbon-fibre-filled polyetheretherketone (manufac- tured by ICI, trade name Victrex PEEK 450 CA30). It is a very strong and inert material. Below 50°C it has about half the strength of mild steel (tensile strength, 250MPa) whilst at 250°C it still has a strength (50 MPa) which is higher than the room temperature value of many structural plastics. It has low friction and good wear characteristics, its fatigue life is excellent, and it is suitable for use with most solvents and chemicals. Its tensile strength is scarcely affected by boiling in water at 100°C for 200 days. Its only disadvantage, namely high price, is of little con-

Fig. 6 Photograph of the partially assembled gaterotor with five inserts in position

Fig. 6 Photo de satellite, partiellement assemble, cinq garnitures d'#tanch#it# sont en place

Volume 8 Num6ro 4 Juillet 1985 219

sequence in this application as the amount used is small. Hence, the new design allows the introduction of a plastic which has far more attractive properties than that used in present compressors, and it permits a much wider range of duties.

The small (1 30 mm main rotor diameter) compre- ssor which we are adapting to incorporate the new gate- rotors, to be tested initially on both nitrogen and steam, is virtually complete, but it has yet to be run. Its use as a steam compressor has necessitated modif ication of the bearings, and these have proved troublesome.

Manufacturing cost

Rotors

The new gaterotor design wil l involve significant savings. The machine tool for cutt ing existing plastic stars is very expensive because the contact line on both leading and tailing faces is the intersection between two three-dimensional surfaces. Also extreme pre- cautions are required to avoid stored stresses wi th in the plastic blanks which would manifest themselves after machining.

Casing

The pressure shell for the single-screw compressor is a simple cylinder, and it is compact for a given through- put because the flutes in the main rotor are used twice per revolution. Hence, the casing has the potential of being relatively small and cheap to fabricate.

Considerable Size penalties and complexity are added to casings by the present unloading gear. New electric motors are beginning to appear which offer speed control coupled with greater efficiencies than are achieved with normal a.c. squirrel cage motors. As

soon as the price of these new drives becomes com- petitive the need for unloading gear wil l go.

Bearings

Because bearing loads in the single-screw compressor are l ight the size of the bearings and their mountings can be small, and they can be cheaper than in the twin- screw machine. With new materials becoming avail- able it is becoming increasingly possible to avoid the use of oil and to lubricate the bearings with the liquid phase of the vapour being compressed. Such a development generates further cost savings in the total compressor system.

The only inherent unbalanced load is the thrust on the engaged teeth of the gaterotor. By suitably sizing the lower gaterotor shaft, and by supporting it wi th in a closed chamber, this thrust force can be offset hydro- statically, thus further reducing the bearing problem.

Conclusions

By adopting the new measures described there would appear to be no reason why the isentropic efficiency of the single-screw compressor should not be increased to >80%. Moreover, by coupl ing it to a speed- controlled motor, and eliminating the oil circuit, as well as by other design features, the manufacturing cost could be reduced substantially.

A patent application covering a number of the novel features described above is held by University of Leeds Industrial Services Ltd.

References

1 Chan, C. Y., Haselden, G. G. Proc XV/International Congress of Refrigeration Paris (1983) 2 982-9

2 Hundy, G. F. Proc /nst of Refrigeration (1981/2) 78 61-9; Haselden, G. G. ibid 23-7

3 Chan, C. Y., Haselden, G. G. Proc /nst of Refngeration (1983/4)

220 International Journal of Refrigeration