Redesign of Diving Compressor Maniflods to Avoid Excessive Power Usage: A Case Study

Transcription

1 Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 1976 Redesign of Diving Compressor Maniflods to Avoid Excessive Poer Usage: A Case Study W. Soedel D. Strader B. Mutyala Follo this and additional orks at: Soedel, W.; Strader, D.; and Mutyala, B., "Redesign of Diving Compressor Maniflods to Avoid Excessive Poer Usage: A Case Study" (1976). International Compressor Engineering Conference. Paper This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at Herrick/Events/orderlit.html

2 Redesign of Diving Compressor Manifolds to Avoid Excessive Poer Usage: A Case Study Werner Soedel, Professor of Mechanical Engineering Dennis L. Strader, Graduate Research Assistant Bramahji R. Mutyala, Graduate Research Assistant Ray W. Herrick Laboratories, Purdue University, West Lafayette, Indiana INTRODUCTION Preliminary tests of prototype compressors for an underater breathing system revealed excessive poer usage that appeared to be connected to high pressure build-ups in the compressor cylinders. The compressor design as therefore revieed, the probable cause of the difficulty as identified using analytical approaches and a design modification as suggested. A 35% reduction in poer requirement as the result. This paper presents the ay this as accomplished in terms of a historical case study. By 'historical' is meant that the analysis of the valves, hich at first ere suspected (rongly, as it turned out) of causing the difficulty, is also presented. It is felt that there is merit in this ay of presentation since in some other situations the valves might prove to be the source of misfunction, and not the manifold design. DESCRIPTION OF COMPRESSORS A first prototype compressor as designed and fabricated as a nominal one horsepoer compressor. To of these compressors ill be used in an underater breathing system. They are both attached to an underater diving base, from here on referred to as a diving platform. The supply compressor "pushes" breathing gas out to a diver from the ambient atmosphere of the diving platform against a nominal pressure differential of about 8 psi. The return compressor "pulls" gas from the diver and returns it back to the diving platform against a pressure differential of approximately 35 psi. The diving platform is under an ambient pressure equal to the ater pressure at the depth the platform is located at. For this investigation, the "design" depth of l, feet of sea ater as chosen. The breathing gas is Helium, ith Oxygen and Nitrogen added such that their partial pressures are the same as in the earth atmosphere at sea level. The compressors are of the reciprocating type and are hermetically sealed by stainless steel bellos. The valves that ere selected after extensive preliminary testing by the designer ere reed valves. They consist of multiple finger type reeds riveted to a seat plate. Each finger seals off a circular port. Inlet and outlet valving is achieved by installing reeds on opposite sides of a common seat plate. Teflon gaskets seal the inlet and outlet reed sections from each other and from the ambient atmosphere. Valves open into, respectively from, discharge nd suction plenum chambers. From these chambers, pipes convey the breathing gas to other parts of the system. PROBLEMS ENCOUNTERED WITH FIRST PROTOTYPE. The prototype compressor as tested in a specially designed pressure chamber. It as found that the poer consumption as almost tice the value expected. As a matter of fact, a larger drive motor had to be used to complete the tests. The flo rate as satisfactory. A pressure transducer as installed for cylinder pressure measurements and shoed a peak-to-peak pressure difference of a bout 185 psi instead of the discharge minus suction pressure difference of about 8CJ psi. A typical measurement is sketched in Figure 1 and compared to an ideal indicator diagram. The area enclosed by the pressure volume trace is equal to the indicated energy per cycle and is almost tice that of the ideal trace. 326

3 It as therefore concluded that if the reason of the overpressure could be found then this ould also serve as the reason for the excessive poer requirement. BREATHING GAS PROPERTIES To start analytical detective ork, the properties of the breathing gas ere needed. In the folloing, the subscripts, N and H denote oxygen, Nitrogen and Helium. By the la of mixtures [1], Also of interest is that v(at Ptotal) y(at 14.7 psi) 1 1 if e assume that the temperature is the same. The gas constant of the gas mixture is given by Where Rtotal = goro + gn + gh r N Mtotal p Since Po and pn are knon, as ell as Ptotal' hich s given by the depth, here r = PH = Ptotal - Po - PN The molecular eight is Mtotal = ro MO + rn + rh The specific eight is Ptotal The specific heats are c = g c + g c + c p N N ghph total P P cv = gocvo + gncvn + ghcvh total The adiabatic number is therefore k total c ptotal cv total The properties of the individual gases at atmospheric pressure are summarized [2'1 Type M at Ft-lb/ of Gas lb/p Mole 14.7 psi lb- "R lb/t 3 R cp cv BTU/lb-"R BTU/lb- R K Oxygen, ? Nitrogen, N2 Helium He 327

4 Thus, given the folloing values at a suction pressure of 459 psi (this corresponds to a diving platform location at 1 feet): v total.43 At discharge v total Rtotal ktotal "' pressure of lb m ft 3 ft lbf lb m 541 psi, e lbm ktotal "" 1.65 ft or get: That this is different enough from the values e ould get for pure Helium can bee seen from Figures 2 to 5. Shon in Figure 6 is the speed of sound. At the suction and discharge condition it is: cd "' 3573 in sec in sec The speed of sound as calculated from: c VALVE ANALYSIS ktotal P total 386 Ytotal (at Ptotal) First, an analysis is presented hose aim is to establish average Mach numbers of flo through the valves. These Mach numbers are a measure of pressure drop, valves ith M>.2 being possibly unacceptable and valves ith M<.2 being possibly acceptable. Tne volumetric efficiency is (1] v v 1- For the case under investigation V clearance volume "'.84 in 3 c V "" sept volume = 5.3 in 3 pd = nominal discharge pressure ps nominal suction pressure lb 541 f. 2 1-EP 459 f n= polytropic coefficient = k = 1.65 This gave =.98 hich had to be considered good. Even hile the clearance volume is large, the pressure ratio is nearly unity, hich negates the large clearance volume effect. in 2 The volume taken in at suction condition is: v 8 "' v = 5.21 in 3 Thus, the mass delivered per cycle is: here m specific eight at suction=.43 lbm ft 3 Ydspecific eight at discharge.461 Thus, m =.122 lb /cycle. The volume that is discharged m is: y._.... Yd v s The time the valves are open is estimated to be for the suction valve here Thus, ts valve, t s 3 n n = rotational speed "" 1725 RPM.17 sec. For the discharge 27 n.16 sec lb ft 3 328

5 Flo areas are a function of valve lift. We may, hoever, argue that the valve reeds ill very quickly reach their limit displacement. Thus, e take the area that shos the most flo restriction under full lift condition. This gave for both suction and discharge valves: The mean velocities are therefore: v c v s At v = d s s 766 in sec i.!l s.,c The average Mach numbers are, therefore: M s vd Md = = Oo2 cd These Mach numbers are quite small and it had to be concluded, therefore, that the designed valve flo areas are sufficiently large and cannot be held responsible for the large measured pressure build-ups. This conclusion as later verified by actually calculating approximate pressure build-ups due to valve action alone by use of an existing computer program. This pr gram as constructed according to the principles laid don in references [3,4,5]. It incorporated the dynamics of the valve reeds and utilized the actual instantaneous flo areas. Inputs to the program ere the geometries of the compressor, the gas properties, instantaneous flo and force area [3,4] and the fundamental natural frequencies and modes of the valve reeds. The natural frequency of a reed for both suction and discharge as determined to be 37 Hz. This agreed ell ith the frequency of the ave ripples that shoed up on the cylinder '' pressure data taken. Flo and force areas ere almost identical for suction and discharge. Results verified the classical analysis. The valves ere not responsible for the high pressure build-ups. A sketch of a typical pressure-volume diagram obtained by the program is given in Figure 7. The pressure peaks at the beginning of discharge and suction are due to the effects of the inertia of the valve reeds. Once the reeds have moved out of the ay, the overpressure appears to be of very reasonable magni tud ":'. The mass delivered per cycle calculated by the program as m-=.121 lb /cycle, only slightly loer than the idealmvalue of m =.122 lb /cycle hich as calculated before ith thw classical approach. PLENUM PRESSURE CHANGES Suspicion centered therefore on the plenum designo For instance, it as felt that the measured cylinder pressure increase during discharge might be due to an immediate increase in discharge plenum pressure due to the inertial properties of the gaso This effect as encountered in a similar fashion in refrigeration compressors 16,7,8,9,11. Unfortunately, computer programs that ere developed in this area ere all tailored to certain compressor types and a modification to the needs of this study ould have exceeded the time and budget limitations Rather than going to a measurement program, it as decided to use a simplified formula for pressure increases in the plenums by making the assumption that mass flo into the plenum is a knon quantity not influenced by the pressure increase itself. Development of the formula is given elsehere in these proceedings. According to it, the plenum pressures are given by p{ A e-bt(ebt_ 1 ) < t < T here A and here c m T A v A e-i3t(ebt_ 1 ) T < t em gta v B ca speed of sound [in/sec] mass per cycle [lbm/cycle] time valve is open [sec) pipe crossectional area [in ] plenum volume The folloing values ere taken for the discharge system c = 357 in/sec A =.31 in2 v.81 in 3 T "' m.122 lbm/cycle g := 386 injsec2.157 sec 2 329

6 The result is an almost immediate over pressure of 23.5 psi, lasting during the entire opening of the valve, hich has to be matched by the cylinder pressure so that the valve ill open at all. For the suction valve the values ere c = 3541 in/sec = A.31 in 2 v.81 in 3 ::: T.174 sec m.122 lb /cycle m 2 g 386 in/sec The result is an almost immediate suction plenum pressure change of -21 psi. The cylinder pressure during suction ill have to be loer than that in order for the valves to open. This is quite conclusive, especially if e remember that resonance conditions in the pipe may change the plenum pressure even further. Therefore, the conclusion as clearly that the plenum volumes had to be enlarged. Plenum pressure curves for plenum sizes of.81, 1, 1 in 3 are shon in Figures 8 and 9, to give the reader an appreciation of ho much larger the plenums actually had to be in this case. The formula also explained the ratio of over pressure beteen 6 feet and 1 feet diving depth, hich as measured to be, for 8 psi compression pressure. r =.64 It is, for small plenum sizes, theoretically given by r = (em) 6 feet (em) 1 feet The mass per cycle delivered at 6 feet is roughly m (v 6) m6 = 1 v 1 Thus, the theoretical value as found to be r = This agreed value. (cy) 6 (cv)looo ell ith =.65 the experimental... SIZE OF REQUIRED PLENUM VOLUMES If the formula used in the previous chapter is evaluated at valve closing time t = T, e get as maximum over pressure (or under pressure) -BT Pmax = A (1 - e ) The required volume for a certain alloable value of p is therefore here v max ln[ c l - c cat A em gta For instance, for an alloable over pressure of Pmax = 5 psi in the discharge plenum, e need for the case under investigation a volume V = 734 in3. Note that only as V + oo ill p +. max Plots of required volumes as function of Pmax are given in Figure 1. PRELIMINARY RESULTS FOR COMPRESSOR WITH LARGER PLENUMS The plenum chambers of the compressor 'i'tere redesigned to havj larger volumes. For chambers of 4 in size, the poer consumption as reduced by about 35%. Measurements [11] on a multi-cylinder unit shoing total overpressure (defined as the difference beteen total pressure variation and ideally expected pressure variation) and the total poer consumption (this includes the drive motor, friction and other losses) as function of plenum volume are shon in Figure 11. The figure shos that the original plenum as clearly too small. These measurements ere made after the theoretical reasoning led to a redesign of the plenums. Thus, the value of sound theoretical approaches to compressor design in the draing board stage as demonstrated. 33

7 SUMMARY A case study as presented that traced the excessive poer consumption of a diving compressor to gas inertia effects in the discharge and suction plenums. Since the compressor as by all reasonable standards ell designed, it as felt that presentation of such a case study as orthhile. SimilarlO. effects may be (and have been) encountered in the design of other compressors. This case study also presents the first practical application of an approximate equation for gas inertia induced pressure built-up in plenums. Development of this formula is 9. Singh, R., and Soedel, W., "A Revie of Compressor Line Pulsation Analysis and Muffler Design Research: Part II - Analysis of Pulsating Flos," Proceedings of the 1974 Purdue compressor Technology conference, 1974, pp Soedel, W., "On the Simulation of Anechoic Pipes in Helmholtz Resonator Models of compressor Discharge Systems," Proceedings of the 1974 Purdue Compressor Technology Conference, 1974, pp presented elsehere in these proceedings. 11. Bentz, R.C., Project Engineer, Naval REFERENCES Coastal Systems Laboratory, "Personal Communication", March Sass, F., and Bouche, Ch., "Dubbels Taschenbuch fur den Maschinenbau," Springer Verlag, Faires, V.M., "Thermodynamics," Macmillan, London, 5th Edition, Soedel,., "Introduction to the Computer Simulation of Positive Displacement Compressors," Short Course Text, Purdue University, ACKNOWLEDGEMENTS The authors ould like to acknoledge the help and guidance received from Mr. R.C. Bentz, Project Engineer, Naval Coastal Systems Laboratory, and Mr. P.L. Fontecchio, Senior Project Engineer, Metal Bellos Company. 4. Hamilton, J.F., "Extensions of Mathematical Modeling of Positive Displacement Type Compressors," Short Course Text, Purdue University, soedel,., and Wolverton, s., "Anatomy of a Compressor Simulation Program," Short Course Text, Purdue University, Soedel,., Padilla-Navas, E., and Kotalik, B.D., "On Helmholtz Resonator Effects in the Discharge System of a To-Cylinder Compressor," Journal of Sound and Vibration, Vol. 3, No. 3, 1973, pp Elson, J.P., and Soedel, W., "Simulation of the Interaction of compressor Valves ith Acoustic Back Pressures in Long Discharge Lines," Journal of Sound and Vibration, Vol. 34, No. 2, 1974, pp Singh, R., and Soedel, W., "A Revie of Compressor Line Pulsation Analysis and Muffler Design Research: Part I - Pulsation Effects and Muffler Criteria," Proceedings of the 1974 Purdue Compressor Technology Conference, 1974, pp

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