Mutyala, B.

Soedel, W.

Strader, D.

English

Purdue E-Pubs

Purdue UniversityPurdue e-PubsInternational Compressor Engineering Conference School of Mechanical Engineering1976Redesign of Diving Compressor Maniflods toAvoid Excessive Power Usage: A Case StudyW. SoedelD. StraderB. MutyalaFollow this and additional works at: https://docs.lib.purdue.edu/icecThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.htmlSoedel, W.; Strader, D.; and Mutyala, B., "Redesign of Diving Compressor Maniflods to Avoid Excessive Power Usage: A Case Study"(1976). International Compressor Engineering Conference. Paper 210.https://docs.lib.purdue.edu/icec/210Redesign of Diving Compressor Manifolds to Avoid Excessive Power 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 underwater breathing system revealed excessive power usage that appeared to be connected to high pressure build-ups in the compressor cylinders. The compressor design was therefore re-viewed, the probable cause of the difficul-ty was identified using analytical ap-proaches and a design modification was sug-gested. A 35% reduction in power require-ment was the result. This paper presents the way this was accom-plished in terms of a historical case study. By 'historical' is meant that the analysis of the valves, which at first were suspected (wrongly, as it turned out) of causing the difficulty, is also presented. It is felt that there is merit in this way of presentation since in some other situa-tions the valves might prove to be the source of misfunction, and not the manifold design. DESCRIPTION OF COMPRESSORS A first prototype compressor was designed and fabricated as a nominal one horsepower compressor. Two of these compressors will be used in an underwater breathing system. They are both attached to an underwater 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 plat-form against a nominal pressure differen-tial of about 80 psi. The return compres-sor "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 water pres-sure at the depth the platform is located at. For this investigation, the "design" depth of l, 000 feet of sea water was 326 chosen. The breathing gas is Helium, with Oxygen and Nitrogen added such that their partial pressures are the same as in the earth at-mosphere at sea level. The compressors are of the reciprocating type and are hermetically sealed by stain-less steel bellows. The valves that were selected after extensive preliminary testing by the designer were 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, re-spectively 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 was tested in a specially designed pressure chamber. It was found that the power consumption was almost twice the value expected. As a mat-ter of fact, a larger drive motor had to be used to complete the tests. The flow rate was satisfactory. A pressure transducer was installed for cylinder pressure measurements and showed 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 indica-tor diagram. The area enclosed by the pressure volume trace is equal to the in-dicated energy per cycle and is almost twice that of the ideal trace. It was therefore concluded that if the reason of the overpressure could be found then this would also serve as the reason for the excessive power requirement. BREATHING GAS PROPERTIES To start analytical detective work, the properties of the breathing gas were needed. In the following, the subscripts 0, N and H denote oxygen, Nitrogen and Helium. By the law of mixtures [1], Since Po and pN are known, as well as Ptotal' which ~s given by the depth, PH = Ptotal - Po - PN The molecular weight is Mtotal = rO MO + rN ~ + rH ~ where r = 0 Ptotal The specific weight is Also of interest is that p v(at Ptotal) ~ y(at 14.7 psi) 1~~~1 if we assume that the temperature is the same. The gas constant of the gas mixture is given by Rtotal = gORO + gN~ + gH~ Where r ~ N Mtotal The specific heats are c = g c + g c + c p 0 0 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 lb/~t3 R cP cv Type M at Ft-lb/ BTU/lb-"R BTU/lb-0 R K of Gas lb/P Mole 14.7 psi lb- "R Oxygen, 32.0 0.083 48.3 0.219 0.157 1.40 0? Nitrogen, 28.0 0.073 55.2 0.248 0.178 1.40 N2 Helium 4.0 0.010 386.0 1.241 0.745 1.67 He 327 Thus, given the following values at a suc-tion pressure of 459 psi (this corresponds to a diving platform location at 1000 feet): v total 0.403 lb m ft 3 Rtotal 311 ft lbf At discharge v total ktotal "' pressure of lb m 1.65 541 psi, we lbm 0.461 ~-3 ft 320 ktotal "" 1.65 oR get: That this is different enough from the values we would get for pure Helium can bee seen from Figures 2 to 5. Shown in Figure 6 is the speed of sound. At the suction and discharge condition it is: in sec cd "' 35730 in sec The speed of sound was calculated from: c VALVE ANALYSIS ktotal P total 386 Ytotal (at Ptotal) First, an analysis is presented whose aim is to establish average Mach numbers of flow through the valves. These Mach num-bers are a measure of pressure drop, valves with M> 0.2 being possibly unacceptable and valves with M<0.2 being possibly ac-ceptable. 328 Tne volumetric efficiency is (1] v 1- ____£ v For the case under investigation V ~ clearance volume "' 0.84 in3 c V "" swept volume = 5.3 in3 pd = nominal discharge pressure ps nominal suction pressure lb 541 __ f . 2 1-EP 459 f in 2 n= polytropic coefficient = k = 1.65 This gave ~ = 0.98 which had to be con-sidered good. Even while the clearance volume is large, the pressure ratio is nearly unity, which negates the large clearance volume effect. The volume taken in at suction condition is: v8 "' ~v = 5.21 in3 Thus, the mass delivered per cycle is: m where lbm specific weight at suction= 0.403 ft 3 lb Yd~specific weight at discharge~ 0.461 ~ ft 3 Thus, m = 0.00122 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 where t s 30 n n = rotational speed "" 1725 RPM Thus, ts valve, 0.017 sec. For the discharge 27 n 0.016 sec Flow areas are a function of valve lift. We may, however, argue that the valve reeds will very quickly reach their limit dis-placement. Thus, we take the area that shows the most flow restriction under full lift condition. This gave for both suc-tion and discharge valves: The mean velocities are therefore: v c v s ~At s s v = d 766 in sec 741 --i.!l s.,c The average Mach numbers are, therefore: M s vd Md = = Oo02 cd These Mach numbers are quite small and it had to be concluded, therefore, that the designed valve flow areas are sufficiently large and cannot be held responsible for the large measured pressure build-ups. This conclusion was later verified by ac-tually calculating approximate pressure build-ups due to valve action alone by use of an existing computer program. This pr~ gram was constructed according to the prin-ciples laid down in references [3,4,5]. It incorporated the dynamics of the valve reeds and utilized the actual instanta-neous flow areas. Inputs to the program were the geometries of the compressor, the gas properties, in-stantaneous flow and force area [3,4] and the fundamental natural frequencies and modes of the valve reeds. The natural fre-quency of a reed for both suction and dis-charge was determined to be 307 Hz. This agreed well with the frequency of the wave ripples that showed up on the cylinder '' pressure data taken. Flow and force areas were almost identical for suction and dis-charge. Results verified the classical analysis. The valves were 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 dis-charge and suction are due to the effects of the inertia of the valve reeds. Once 329 the reeds have moved out of the way, the overpressure appears to be of very reason-able magni tud ":'. The mass delivered per cycle calculated by the program was m-=0.00121 lb /cycle, only slightly lower than the idealmvalue of m = 0.00122 lb /cycle which was calculated before with thW classical approach. PLENUM PRESSURE CHANGES Suspicion centered therefore on the plenum designo For instance, it was felt that the measured cylinder pressure increase during discharge might be due to an imme-diate increase in discharge plenum pres-sure due to the inertial properties of the gaso This effect was encountered in a similar fashion in refrigeration compres-sors 16,7,8,9,101. Unfortunately, computer programs that were developed in this area were all tailored to certain compressor types and a modifi-cation to the needs of this study would have exceeded the time and budget limita-tions • Rather than going to a measure-ment program, it was decided to use a simplified formula for pressure increases in the plenums by making the assumption that mass flow into the plenum is a known quantity not influenced by the pressure increase itself. Development of the formula is given else-where in these proceedings. According to it, the plenum pressures are given by p~{ A e-Bt(eBt_1 ) 0 < t < T A e-i3t(eBT_1 ) T < t where A em B cA gTA v and where c m T A v speed of sound [in/sec] mass per cycle [lbm/cycle] time valve is open [sec) 2 pipe crossectional area [in ] plenum volume The following values were taken for the discharge system c = 35700 in/sec A = 0.31 in2 v 0.81 in3 T "' 0.0157 sec m 0.00122 lbm/cycle g := 386 injsec2 The result is an almost immediate over pressure of 23.5 psi, lasting during the entire opening of the valve, which has to be matched by the cylinder pressure so that the valve will open at all. For the suc-tion valve the values were c = 35410 in/sec A 0.31 in 2 = v 0.81 in 3 ::: T 0.0174 sec m 0.00122 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 will have to be lower than that in order for the valves to open. This is quite conclusive, especially if we remember that resonance conditions in the pipe may change the plenum pressure even further. Therefore, the conclusion was clearly that the plenum volumes had to be enlarged. Plenum pressure curves for plenum sizes of 0.81, 10, 100 in3 are shown in Figures 8 and 9, to give the reader an appreciation of how much larger the plenums actually had to be in this case. The formula also explained the ratio of over pressure between 600 feet and 1000 feet diving depth, which was measured to be, for 80 psi compression pressure. r = 0.64 It is, for small plenum sizes, theoretical-ly given by (em) 600 feet r = (em) 1000 feet The mass per cycle delivered at 600 feet is roughly m (v 600) m600 = 1000 v1000 Thus, the theoretical value was found to be r = This agreed value. (cY) 600 (cv)lOOO well with = 0.65 the experimental ... 330 SIZE OF REQUIRED PLENUM VOLUMES If the formula used in the previous chapter is evaluated at valve closing time t = T, we get as maximum over pressure (or under pressure) -BT Pmax = A (1 - e ) The required volume for a certain allowable value of p is therefore max v where c ln[ l -c cAT A em gTA For instance, for an allowable over pressure of Pmax = 5 psi in the discharge plenum, we need for the case under investigation a volume V = 734 in3. Note that only as V + oo will p + 0. max Plots of required volumes as function of Pmax are given in Figure 10. PRELIMINARY RESULTS FOR COMPRESSOR WITH LARGER PLENUMS The plenum chambers of the compressor 'i'Tere redesigned to havj larger volumes. For chambers of 40 in size, the power consump-tion was reduced by about 35%. Measurements [11] on a multi-cylinder unit showing total overpressure (defined as the difference be-tween total pressure variation and ideally expected pressure variation) and the total power consumption (this includes the drive motor, friction and other losses) as function of plenum volume are shown in Figure 11. The figure shows that the original plenum was clearly too small. These measure-ments were made after the theoretical rea-soning led to a redesign of the plenums. Thus, the value of sound theoretical ap-proaches to compressor design in the draw-ing board stage was demonstrated. SUMMARY A case study was presented that traced the excessive power consumption of a diving compressor to gas inertia effects in the discharge and suction plenums. Since the compressor was by all reasonable standards well designed, it was felt that presentation 9. Singh, R., and Soedel, W., "A Review of Compressor Line Pulsation Analysis and Muffler Design Research: Part II -Analysis of Pulsating Flows," Proceed-ings of the 1974 Purdue compressor Technology conference, 1974, pp. 112-123. of such a case study was worthwhile. SimilarlO. effects may be (and have been) encountered Soedel, W., "On the Simulation of Anechoic Pipes in Helmholtz Resonator Models of compressor Discharge Systems," Proceedings of the 1974 Purdue Compres-sor Technology Conference, 1974, pp. 136-140. 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 presented elsewhere in these proceedings. 11. Bentz, R.C., Project Engineer, Naval Coastal Systems Laboratory, "Personal Communication", March 1976. REFERENCES 1. Sass, F., and Bouche, Ch., "Dubbels Taschenbuch fur den Maschinenbau," Springer Verlag, 1970. 2. Faires, V.M., "Thermodynamics," Macmillan, London, 5th Edition, 1970. 3. Soedel, w., "Introduction to the Com-puter Simulation of Positive Displace-ment Compressors," Short Course Text, Purdue University, 1972. 4. Hamilton, J.F., "Extensions of Mathe-matical Modeling of Positive Displace-ment Type Compressors," Short Course Text, Purdue University, 1974. 5. soedel, w., and Wolverton, s., "Anatomy of a Compressor Simulation Program," Short Course Text, Purdue University, 1974. 6. Soedel, w., Padilla-Navas, E., and Kotalik, B.D., "On Helmholtz Resonator Effects in the Discharge System of a Two-Cylinder Compressor," Journal of Sound and Vibration, Vol. 30, No. 3, 1973, pp. 263-277. 7. Elson, J.P., and Soedel, W., "Simulation of the Interaction of compressor Valves with Acoustic Back Pressures in Long Discharge Lines," Journal of Sound and Vibration, Vol. 34, No. 2, 1974, pp. 211-220. 8. Singh, R., and Soedel, W., "A Review of Compressor Line Pulsation Analysis and Muffler Design Research: Part I -Pulsation Effects and Muffler Criteria," Proceedings of the 1974 Purdue Compres-sor Technology Conference, 1974, pp. 102-111. 331 ACKNOWLEDGEMENTS The authors would like to acknowledge 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 Bellows Company. 600 ~ N !:! 550 ·.-i " 4-l ..Q rl Ll.J a: ::> 500 (f) (f) Ll.J a: 0... a: Ll.J 0 450 z ..J >-(.__) 480 PTOTAL [PSI 1 1000 900 800 700 600 500 400 300 200 100 0 ~ 0 LossEs 1.0 2.0 3.0 4.0 5.0 6.0 7.0 CYLINDER VOLUME liN3J FIGURE l. TYPICAL f1EASURED INDICATOR DIAGRAM HELIU~1 (PARTIAL PRESSURE) 1000 2000 3000 DEPTH [FTJ FiGURE 2. PRESSURE OF BREATHING GAs 332 0 0:::: J-z <:( t-(.f) z 300..,......_ __ 3 100~---------(.f) <:( ~ -+--------·-·-·· 0 ----------------~----------------~.----------------~ 0 1000 2000 1'<\t;: '8 +---·--- . ----- ' -....._ :E: DEPTH [FT] FIGURE 3. GAS CONSTANT ~ I 7+---------·----·--- ----------·---------......J c::c 1- ,6 0 t-1-<( '5 +-----------·---·-- --~--· --- ---- . I 3-t------- ---.2 .1 0 1000 DEPTH [FTl 2000 FIGURE 4~ SPECIFIC r1ASS 333 3000 3Cl00 210 1.9 ::.::: 1.8 (/) I-i:5 1. 7 ::c u ~ 1.6 ...... u w w & 1.5 LL 0 w .,. 0 1.4 -I-<r: 0::: 1.3 1.2 111 0 -+-------- j ____ ..:---,........-~-:--~------- -- ----/ ; c - -- 1]~}:-/ I PTOTAL - --·- -- ...... ;r---------~---- - -·---- -- ' --- - .~r';, / - ' r------ -- _J t-- -I ' ! ---- .9~1-I  1----- -- --- I ' "' I K - :--- ---1---i- +--·=.:::-=-.: ..:....:...--~-::;;;;;=~--.8 -l ;::: 0 .7 :t"" 1 u -- --- -- ---.....-~ - --J-------- ---· --- -.. . -----+ I 6 .'~ -~ TT __ _:./.~. -; ----VTOTAL ·0 1--'--t----------r----------·--------· 1- I 5 if-I l --~--- ---~f I ---- 1 _______ T_ --1 __ _ __;______ 1/ -------- -• --+------·- -- -- -- .. - -- ·----1000 2000 DEPTH [FTl FIGURE 5~ SPECIFIC HEATS Ul 1-4, o¢ I UJ ::c u 13 ~ -u w .2& II 3000 -· -~ --~---u UJ V> -:z 0 0 0 0 0 0 .. .. .. u 0 0 0 ~ !'('\ N 335 0 ___ , __________ ~-------i I ! i I i I I I I - J ___ I I I j I 0 0 0 ....--1 ------0 !'('\ 0 0 0 N 0 0 0 ....--1 0 0 z => 0 U) u_ ...... 0 1-u_ 0 LU w :I: 0... 1- U) 0... w ~ r..6 UJ a::: ::::::1 (!) u. 600 N s:: ·.-! ........ 550 ~ .Q ...... ~ Ul 0::: ::::l U) 500 U) l.lJ 0::: CL 0::: Ul w Cl z ...... w 0'1 450 ....I >-u 400 I ;1EASURED ,_J-- LossEs ONLY I ,""" / . , \ - -~ '-~ ''-_, ...._. ._, ~ -_,. 1.0 2,0 3,0 4.0 5,0 CYLINDER VOLUME [IN3] 6.0 @ Ps 7.0 fiGURE ], EFFECT OF VALVES ON INDICATOR DIAGRAM LossEs w w -.1 22 ~~ V=-a'. 83 _,.....--· ./ 1\ /v = 10 I\_ VALVE CLosEs I t 20 . ';:: / // ~16 I / , i 14 ' // \\ ·~12 I I ' \ ,UJ . I I ,y = 100 \ \ ;~ 10 ·~ I ~I \ ~ I • ·'\_ ~a./' I \ '-~ I ' '-~ 6 I I ·\ ' ~ I I ~ .54 I ' " 2 vrVALVE OPENS '\ ' '-18 ,, __ ~----0 ' ·;005 • ;010 ' .015 .pzo .025 .030 TIME [SEC] FIGURE g, DISCHARGE PRESSURE INCREASE w w 00 .::zz -20 Jrv = 0,83 ,.,-- = r-VALVE CLOSES " / -Is -u · v = 10 I /--\. "~ -16 I ,/_./' \\ :: -14 I // , \\ ~ ~ \ ~· -12 1 / v = 100 \ ~ I / \ " ~ -10· I I \ " ~ - s~ I " ~ J I ' ' 2-6·~~ I \ ', r / ' u \ ' ~ - 4r - 1 j '~ -:· "rt VALVE OPENS "'''-. --,005 .010 .015 .020 .025 .030 TIME [SEC] fiGURE 9. SUCTION PRESSURE DECREASE 0 0 0 N ::;:;;o-' -::;;-0 0 L1"'' rl ~ 0 0 0 rl 339 ::;:: ::::l z: UJ _J 0.... UJ ~ 0::: <( :c u (I) p 0 0 U\ :E ::::l z: UJ ._J 0.... z 0 I-u ::::l (/) 0 UJ N ::;:: ::::l _J 0 > ::;::: ::::l z: UJ _J L.t"':;. 0.... rl (I) >-0.. 0::: <( (I) X (I) <( UJ ::;::: u Cl.. UJ z a a rl rl UJ 0::: ::::l ~ LL L1"'' w oJ>. 0 N .: 150 ~ 125 '1-l .Q .-1 ~ 100 :::J U) U) w 0::: ~ 75 w > 0 __J ;::: 50 0 f--25 0 : -:~ c• • . . , • " " '• • • · i •~. :;;;I C • ·•· -\ ~c · ::1 ' . "11 ~~:~:·~·)I;:~;;.:~~-. ~DRIG INAL DESJGU . . .: . •·•. -···I·"'-~-" •i :c:c c.·;•• cc' ..... •I . CL:" 5 10 . 15 20 25 30 35 40 750 .PLENUM VOLUME [~n3 1 FIBURE 11 MEASURED OVERPRESSURE AND POWER REDUCTION AS FUNCTION OF PLENUM SIZE. 6 5 4 3 2 1 0 ~ 0::: w ::::: 0 a_ 

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

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

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