NUMERICAL INVESTIGATION OF HEAT TRANSFER ON SCREW COMPRESSOR ROTORS

Transcription

1 NUMERICAL INVESTIGATION OF HEAT TRANSFER ON SCREW COMPRESSOR ROTORS N Stosic, I. K. Smith an A. Kovacevic Centre for Positive Displacement Compressor Technology, City University, Lonon EC1V OHB, U.K, n.stosic@city.ac.uk Key wors: Heat Transfer, Dry Screw Compressor, Water Injection Abstract. Since ry screw compressor rotors an housing are subjecte to high temperatures which cause their eformation, they either may not operate at high pressure ratio, or they must be coole. However, the gas temperature is high only in the high pressure region of the screw compressor therefore the omain where the heat is transferre to the rotors is limite to only a small portion of the rotors an housing. Also, since the rotors revolve at high spees while resiing only briefly within areas of ifferent gas temperatures uring one cycle, the rotor temperature becomes virtually uniform across any cross sectional area perpenicular to the rotor axis an its value is somewhere between the highest an lowest gas temperature at that cross section area. At the same time, ue to the relatively high thermal conuctivity of the compressor components, which are mae of metal, heat transfer by conuction is consiere substantial an the rotor boy temperature attaine is a result of a balance between the heat receive from the gas an its issipation in regions of lower gas temperature. Consequently, it appears that rotor cooling is require only in the compressor high temperature region to keep rotor temperatures at a reasonable level. Therefore, an effective means of cooling the rotors coul be to inject a small quantity of flashing liqui, preferably water into the casing, at the high pressure port en in any circumferential position. The liqui woul then impinge on the rotors at a rate such that it woul be instantly evaporate by contact with them. To confirm these principles an quantify the heat transfer rate an require flow rate of liqui injecte for rotor cooling, a complex numerical investigation by using a CFD coe has been performe. The results inicate that ry compressors may run at pressure ratio up to 8:1. This is substantially higher than the normal pressure ratios attainable in such machines. It is also shown that ue to the high rotational spee an intermittent passing through hot an col gas areas, the rotor temperature is far lower than that of the gas. Since the heat transfer rate between the gas an the rotors is very low, it is possible to cool the rotors by only relatively small quantities of flashing flui, such as water. The experimental investigation was performe to confirm these estimations. The result of this investigation is that only minor moification is require for oil free compressors to be mae to operate with much higher pressure ratios in a single stage.

2 NOMENCLATURE c - concentration f - boy force h - enthalpy m - mass q - heat flux p - pressure s - control volume surface s - source/sink S - strain tensor t - time T - stress tensor T - temperature v - velocity V - volume x - spatial coorinate - ensity 1 INTRODUCTION The present worl annual prouction rate of positive isplacement compressors is in excess of 200 million units, while approximately 17% of the worl s electric power prouction is require to rive them in inustrial, commercial an omestic applications. The majority of these are reciprocating machines but many other types, such as screw compressors, play a significant role. 1a) View from Front an Top 1b) View from Bottom an Rear Figure 1: Screw Compressor Main Components The main avantage of screw compressors, over other types of positive isplacement machine, is the pure rotary motion of their moving components. This enables them to attain higher rotational spees an hence to be more compact, while maintaining high efficiencies an

3 elivery rates over a wie range of operating conitions with less wear an hence a longer service life. Thus, typically, they are up to five times lighter than reciprocating compressors of the same capacity an their service life is nearly ten times longer. Consequently an increasing proportion of positive isplacement compressors sol an currently in operation are of this type. Suction Area Discharge area Figure 2: Screw Compressor Main Components Screw compressors consist essentially of a pair of meshing helical lobe rotors, containe in a casing. Together, these form a series of working chambers, as shown in Fig 1, by means of views from opposite ens an sies of the machine. The ark shae portions show the enclose region where the rotors are surroune by the casing an compression takes place, while the light shae areas show the regions of the rotors that are expose to external pressure. The large light shae area in Fig 1a) correspons to the low pressure suction port. The small light shae region between shaft ens B an D in Fig 1b) correspons to the high pressure ischarge port. Amission of the gas to be compresse occurs through the low pressure port which is forme by opening the casing surrouning the top an front face of the rotors. Exposure of the space between the rotor lobes to the suction port, as their front ens pass across it, allows the gas to fill the passages forme between them an the casing. Further rotation then leas to cut off of the port an progressive reuction in the trappe volume in each passage, until the rear ens of the passages between the rotors are expose to the high pressure ischarge port. The gas then flows out through this at approximately constant pressure. Machines of this type are normally classifie into two main types; namely: i) oil injecte an ii) oil free. The bulk of screw compressors manufacture are of the oil injecte type. In these, a relatively large mass, but small volume of oil is amitte into the compressor, after amission of the air or gas is complete, an remains in contact with the gas being compresse, as a isperse liqui, which is then ischarge with the gas. After leaving the compressor, the oil is separate from the gas, coole an then reinjecte. The riving force for reinjection is the

4 pressure ifference between the ischarge gas an that between the meshing rotors, trappe in the compressor immeiately after suction is complete. The oil serves three purposes; namely as a lubricant, as a sealant of the clearances between the rotors an between the rotors an the casing an as a coolant of the gas being compresse. Because of this latter effect, gases can be compresse to pressure ratios of up to about 15:1 in a single stage without an excessive temperature rise. Dry gas compression in screw machines is limite to a pressure ratio of approximately 3:1. This is because the higher gas temperatures of the uncoole gas cause the rotors an housings to eform. It follows that if the rotors were coole, higher pressure ratios woul be possible. To o this effectively, the principles of heat transfer within these machines nees to be properly unerstoo. 2 HEAT TRANSFER WITHIN SCREW COMPRESSOR Firstly, it must be appreciate that the gas temperature is only high in the high pressure region of the screw compressor. This occurs where the working chamber volume is greatly compresse. This is in the region of the compressor, immeiately prior to the ischarge port, as shown at the location marke as the ischarge area in Fig 2. Consequently, the area enclosing this volume, from which heat is transferre to the compressor components, is small. Also, the heat transfer coefficient between the gas an the rotors is low. Thus Brok et al, 1980 [1] claim that the heat transfer between gas an compressor elements is negligible. Recktenwal et al, 1986 [4] isagree but still amit that, in energy terms, the heat transfer rate is less than one percent of the total compressor power input. Nevertheless, over a large number of compression cycles, resulting from continuous operation, the temperature rise within the compressor parts can be substantial. Seconly, the gas temperature varies significantly aroun the circumference of the compressor bore in any plane normal to the axis of rotor rotation, especially near the ischarge port where the pressure varies between near suction an ischarge. Despite this, ue to the rapi rotation of the rotors an the poor rate of heat transfer between the gas an the rotors, the rotor temperature is almost constant aroun the circumference. However, the compressor components are mae of metal, which has a relatively high thermal conuctivity. It follows that the main means of heat transfer along the length of the rotors from the high pressure to the low pressure ens is by internal conuction along them with an approximately linear boy temperature istribution in the axial irection. The rotor temperatures attaine are therefore the result of a balance between the heat receive from the gas at high temperature an its rejection to regions at lower temperature. When these consierations are taken into account, an effective means of cooling the rotors coul be to inject a small quantity of flashing liqui, preferably water into the casing, at the axial en corresponing to that of the high pressure port in any circumferential position. The liqui woul then impinge on the rotors at a rate such that, ue to the high heat transfer

5 coefficient it woul instantly evaporate on contact with them. In view of the low heat transfer rate from the gas to the rotors, the liqui mass flow rate require for this woul be of the orer of only a few tenths of one percent of the mass flow rate of the gas being compresse. The liqui woul then separate out from the compresse gas by conensation in the compressor aftercooler, which is a common component of a ry compressor plant. Figure 3: Screw compressor pressure an temperatures To confirm these principles an quantify the heat transfer rate an require flow rate of liqui injection for rotor cooling, an initial stuy of heat an flui flow in a screw compressor was carrie out using a computer coe, base on the assumption of homogenous on one imensional flow of flui through the compressor, etails of which are given by Hanjalic an

6 Stosic, 1997 [2] an Stosic an Hanjalicl, 1997 [5]. The compressor assume, ha a male rotor iameter of 102 mm an a length/iameter ratio of 1.55 rotating at 10,000 rpm, compressing air from 1 to 6 bar. In this case the power input was estimate at 47 kw. Figure 4: Screw compressor volume an heat transfer area The results of the stuy are shown in Figs 3 an 4. The rotor cooling rate was estimate by a trial an error proceure, after a guess, the linear rotor temperature istribution was correcte to balance the heat transferre to the rotors at high temperature regions an from the rotors at low temperature regions. As can be seen, the gas temperature, which is shown by a full line in the case of the coole rotor an by a otte line when the rotor is not coole, attains a peak value of 260 o C. The rotor temperature istribution is shown by two lines, the higher one, when there is no rotor cooling, has a maximum value of 180 o C an the lower one, for the coole rotor has a maximum of only 110 o C. In this case, the heat transfer rate to the rotors at

7 the high temperature region was estimate as only about 100 W an about 1/3 of the heat transferre to the rotors was remove by the water jet impinging on the high temperature area of the rotor. For the calculate conitions, the water flow was g/s, while the air flow was kg/s, giving the mass ratio of water injecte against the air flow of 72 ppm. This is well within the region of humi but not wet air an implies that the injecte water evaporate completely, using its latent heat to cool the rotors. Uner these circumstances, the liqui can be recovere from the compresse gas after cooling in the compressor aftercooler, which is a common element of ry compressor plant. It shoul be note that the water injection rate is so small that the rotor cooling harly affecte the gas ischarge temperature. These results show that by the use of such a simple cooling proceure, oil free compressors can be built to operate with much higher pressure ratios in a single stage. The cost of their manufacture for high pressure applications woul thereby be reuce an their efficiencies increase. It woul also thereby be possible to use twin screw machines to expan gases at much higher temperatures than is presently thought to be possible. It is conclue that by the use of this technique, only minor esign changes are neee to enable oil free compressors to operate with much higher stage pressure ratios D NUMERICAL STUDY OF A SCREW COMPRESSOR HEAT TRANSFER Contemporary evelopments in computational flui ynamics an heat transfer enable the flow processes within screw compressors to be estimate, taking full account of 3-D effects. Numerical calculation of the heat an flui flow through them by this means, improves the unerstaning of the flow phenomena an enables the maximum possible improvements to be mae to the machine esign. An inepenent stan-alone interface program, which connects the screw compressor geometry an a CFD preprocessor, has been evelope by the authors in orer to generate a numerical gri for this purpose. The interface employs a proceure to prouce rotor profiles an an analytical transfinite interpolation metho with aaptive meshing to obtain a fully structure 3-D numerical mesh, which is irectly transferable to a CFD coe. This was require to overcome problems associate with moving, stretching an sliing rotor omains an with robust calculations in omains with significantly ifferent geometry ranges. Some changes have been mae within the solver functions both to enable calculations an to make them faster. These inclue a means to maintain constant pressures at the inlet an outlet ports an consieration of two-phase flow resulting from oil injection in the working chamber. Moifications implemente to the CFD proceure improve solutions in complex omains with strong pressure graients. The pre-processor coe an calculating metho have been teste on a commercial CFD solver to obtain flow simulations an integral parameter calculations. More information on the

8 screw compressor CFD is given by Kovacevic et al 2003 [3]. The program interface calculates the meshing rotor coorinates from given rack or rotor curves, by means of two parameter aaptation, an then calculates the gris for both rotors. It also calculates the gris for the inlet an outlet ports an prepares the control parameters necessary for the CFD calculation of the compressor flui flow. The compressor flow is fully escribe by the mass average equations of continuity, momentum an energy conservation, which are accompanie by the turbulence moel equations an an equation of state. Equations are given for the control volume V boune by surface s in the integral form similar for all conserve properties. They all contain local an convective rates of change on the left han sie an iffusive an source terms on the right han sie. The continuity equation is: t V ( s ) 0 V v v s, S where is the ensity an v is the flui velocity, while v s is the gri velocity. The momentum equation is: t v v( v vs ) s T s f V S S V b V V where T is a stress tensor, an f b is the resultant boy force. mi Since liqui is injecte into a screw compressor, the oil concentration ci, where m is m the overall mass, is calculate from its equation as a passive component, which affects the air in the source term of the mass an enthalpy equation. The concentration equation is: t c V c ( v v ) s q s s V V i S i s S ci V ci q ci an s ci enote the iffusion flux an source or sink of liqui. The transport equation of enthalpy is: hv h( s) h shv t V v v s S q s S V S : v V p V p s pv V v V v s S t V where S is the viscous part of the stress tensor, p is pressure, q h is the heat flux an s h represents the heat source or sink.

9 Figure 5: Gas temperature in vicinity of the screw compressor rotor surface Since screw compressor CFD calculations involve a moving gri, the equation of space conservation is also solve: t V s 0 V v s S Stokes law is a constitutive relation that connects stress an rate of strain, through the viscosity an complements the momentum equation, while the transport equations of concentration an enthalpy are close by Fick s an Fourier s laws respectively. Equations presente are close by the equation of state an accompanie by equations of the appropriate turbulence moel. ( p, T) Results of the numerical calculation of a ry air screw compressor operating between 1 an 3 bars are presente in Figs 5 an 6 where the temperature of gas close to the compressor rotors an the temperature fiel within the rotor metal are given respectively. The results presente confirm that temperature within the screw compressor rotors follows a graual istribution an that it is significantly lower than the temperature of the surrouning gas. This confirms that the metho propose for cooling by impinging the flui to the screw compressor rotors is soun.

10 Figure 6: Temperature fiel in screw compressor rotors 4 EXPERIMENTAL INVESTIGATION An air compressor test rig in the City University Compressor Centre Laboratory, which meets Pneurop/Cagi requirements for screw compressor acceptance tests, was use to check the preicte results. An orinary ry screw compressor, couple to its rive shaft through a gearbox, was moifie to allow water cooling by an impinging jet, with injection in the moerate pressure region at the ischarge en of the compressor rotors, as shown in Fig 2. By this means, the nee for a water pump was avoie but vapour compression of the evaporate liqui was less than if the injection ha been performe in the minimum pressure region. The compressor was riven by an electric motor of 100 kw maximum output, which may operate at variable spee, controlle by means of a frequency converter. This permits the testing of oil-free screw compressors with ischarge rates of up to 16 m 3 /min. Approximately 200 sets of measurements were recore, with the ischarge pressure varie between 3 an 6 bar absolute. The flow of water injecte was kept very low to ensure full evaporation. Measure values were use to calculate compressor flow, power an specific power an water injection rate.

11 The compressor rotors an the water injection hoses are shown in Figs 7 an 8. A typical result for a pressure ratio 5.82, when the compressor was running continuously at an average spee of rpm is use as illustration. In this case, the measure power input was 47kW an the measure air ischarge temperature was 247 o C. Such a pressure ratio an ischarge temperature were far beyon the esign limits of the machine an woul have cause either rotor seizure or severe amage if the rotors ha not been coole. Moreover, the compressor worke well at the higher pressure ratios. The esign an construction of this machine was such that it was consiere unsafe to run it at pressures above 6 bar but the results of these tests were so favourable that further tests are planne to be carrie out at even higher pressure ratios on its improve version. Figure 7: Compressor rotors, housing remove 5 CONCLUSION It has been shown that an effective means of cooling the rotors coul be to inject a small quantity of flashing liqui, preferably water into the casing, at the high pressure port en in any circumferential position. The liqui woul then impinge on the rotors at a rate such that it

12 woul be instantly evaporate by contact with them. Only minor moification is, therefore, require for oil free compressors to be mae to operate with much higher pressure ratios in a single stage. The cost of their manufacture for high pressure applications woul thereby be reuce an their efficiencies also increase. The same principle is possible to use to enable twin screw machines to expan gases with much higher entry temperatures than is presently thought to be possible. Figure 8: Test compressor with the water injection hoses 6 REFERENCES [1] Brok S. V, Touber S an van er Meer J. S, 1980 Moelling of Cyliner Heat Transfer Large Effort, Little Effect, Proceeings of 1984 Purue Compressor Technology Conference, Purue University, west Lafayette IN. [2] Hanjalic K, Stosic N, 1997: Development an Optimization of Screw Machines with a Simulation Moel, Part II: Thermoynamic Performance Simulation an Design Optimization, ASME Transactions, Journal of Fluis Engineering, vol 119, p 664 [3] Kovacevic A, Stosic N, Smith I. K, 2003 Three Dimensional Numerical Analysis of Screw Compressor Performance, Journal of Computer Methos in Applie Mechanics an Engineering, [4] Recktenwal G, W, Ramsey J. W. an Patankar S. V, 1984 Preiction of Heat Transfer in Compressor Cyliners, Proceeings of 1984 Purue Compressor Technology Conference, Purue University, west Lafayette IN. [5] Stosic N, Hanjalic K, 1997, "Development an Optimization of Screw Machines with a Simulation Moel, Part I: Profile Generation, ASME Transactions, Journal of Fluis ngineering, vol 119, p 659