Potential of the single-screw compressor *
G. G. Haselden
Keywords: compressor, gaterotor 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. dynamically balanced components, allowing speeds of rotation which match those of the cheapest motors, and producing low wear; 2. elimination of valves, giving high reliability and reducing losses; 3. compactness, so that the compressor is generally smaller than the driver; 4. efficient 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.
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
Fig. 1 Designation of the leakage paths in the single-screw compressor
F1~7. 1 Localisation des fuites dans le compresseur monovis
o ~r lO
. . . . . . . L I !
............... L2 / "~. . ______ L3 .. ...
I \ . . . . . . L4 . . . . . . . . . . . 1_5
/ "~ .... 1-6 / ~ . . . . . . . . LK . / -,.
............ 2/: ...... . ........
_1 / / I - - . .....
-10 I I I I , I I I I 0 20 40 60 80 100 120 140 160 180
ROTOR ANGLE DEGREE
Fig. 2 Mass leakage rates calculated for a single flute of a compressor running on R22 at 2950 r.p.m., on a - 5 /+ 35C duty. the VR being 2.6, and the clearances 0 .10mm
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 contribution 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 oil-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 significant 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 susceptibility to relative surface movement.
Tests have shown 3 that the effect of relative surface movement on flow through small clearances is generally negligible for gas but can be dominant for liquid leakage. For instance with a 280mm single- screw compressor running at 2950 r.p.m, the maximum surface speed is
. . . . . 1.1
. . . . . . . . . . . L2
. . . . L4 / . . . . . . . . . . "~ ' , - - - - - L5
/ . : i . . . . . . . . . . . . \ _ . . . . . L ,
,..../ - ....... :.".-- . . . . . . . . . . .
/ / / - ' - . . . . . . . ~- . - . ~ ...... " ',
20 ,~ & 4' ,~o ,;o ,4o 40 ,8o ROTOR ANGLE DEGREE
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.
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 fects
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 will 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 ref...