Theoretical Gas Pulsation in Discharge Passages of Rolling Piston Compressor, Part II: Representative Results

Transcription

1 Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 1996 Theoretical Gas Pulsation in Discharge Passages of Rolling Piston Compressor, Part II: Representative Results Y. K. Kim Purdue University W. Soedel Purdue University Follow this and additional works at: Kim, Y. K. and Soedel, W., "Theoretical Gas Pulsation in Discharge Passages of Rolling Piston Compressor, Part II: Representative Results" (1996). 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 THEORETICAL GAS PULSATION IN DISCHARGE PASSAGES OF ROLLING PISTON COMPRESSOR, PART II: REPRESENTATIVE RESULTS Y. K. Kim and W. Soedel School of Mechanical Engineering Purdue University W. Lafayette, IN !.INTRODUCTION Based on the mathematical models derived in part I, several kinds of the results are obtained. The first part of this paper presents the results of parameter studies without the gas pulsations. The purpose of this part is mainly to verify that the mathematical models and the computer program behave logically. The displacements of valve reed, when four parameters are changed one at a time, are presented and discussed. The behavior of valve reed is very important because it is a main source of noise and failure. The second part of this paper is concentrated on the gas pulsations in the discharge manifold of the rolling piston compressor. Pressures in the interior cavities and volume velocities of gas plugs are shown when the dimensions of several parts are changed. The results in this part can be a guide in designing rolling piston compressors because they show how the performance of compressor can be improved, in other word, a decrease of noise level The Fourier spectra of the pressures and volume velocities are also presented to show the effectiveness of the muffler systems. The last set of results shows the effect of a side branch resonator which is attached to the valve cover of the modified rolling piston compressor. We have seen that the total mathematical simulation model involves several differential equations. For our case, we have one second order ordinary differential equation which defines the modal participation factor for the discharge valve reed and two second order ordinary differential equations and one first order ordinary differential equation which are the equations of motion of gas plugs in the gas passages. There are many procedures of solving initial value problems. In our simulation model, the Runge-Kutta method is used, which is one of the most popular procedure of solving systems of first order differential equations. 2. SIMULATION RESULTS WITH GAS PULSATIONS ON DISCHARGE SIDE In this section the results obtained by the simulation program are presented. The results show the performance of the typical rolling piston compressor used in this research and how parameter changes would improve it. During the first two cycles, the iteration process is still converging. It typically reaches steady state after two cycles. All results in this section present the first three cycles for that reason. Readers can assume that the pattern of the result would be repeated once it reaches the steady state. All results are obtained from the same thermodynamic conditions of P.=75.8Psi, Pd=292.8Psi, and T.= R. The program is of course able to predict what happens at other operating conditions. Figures 1 to 4 show how the system reacts when the damping constants are changed. Figures 1 and 2 show the pressure in the cylinder as well as the pressure in the muffler as a function of the crank angle. When the damping constants of the short necks are increased, the gas pulsations both in the cylinder and the valve cover are noticeably reduced. The velocities of the gas plugs (shown in Figure 2 in Part I) are graphically illustrated in Figures 3 and 4. Again, the 619

3 oscillations of the gas plugs are significantly reduced when the damping values are increased. This is important because the discharge gas pulsations can be a significant noise source. They excite the shell of the compressor into vibration and this vibration in turn radiates sound. The reduction of the gas pulsations will decrease the noise of the system and increase the efficiency as well as the life of the compressor. 3. EXPLORATION OF DIRECTIONS FOR DESIGN IMPROVEMENT This chapter consists of two sections: redesign of the typical compressor and design of modified muffler system. First, keeping the standard structure of the typical compressor, we slightly changed the dimensions of three parts such as cross sectional areas, A1, length of the neck, Lt. and volume of valve cover, V~> in order to see if the performance of the compressor can be increased, in other words, a decrease of the noise level. The results are shown and discussed in the first section. In the second section, we attached a small Helmholtz resonator to the valve cover. The schematic of the modified muffler system is shown in Part I. The frequency of the side branch resonator is tuned to three different levels: 450Hz, 600Hz, and 750Hz. Figures 19 to 21 show the results of the modified muffler system. It should be noted that the purpose of this chapter is not the development of a general theory of muffler design but the investigation of possible alternatives to typical compressor design. 3.1 Redesign of Typical Compressor In the following, we have varied the dimensions of the typical compressor _to see if its performance can be improved and again, to verify that the simulation program behaves logically. The results are given in terms of pressures in the interior volumes, volume flow velocity between each volume, and volume flow velocity at the discharge muffler exit. In addition, the Fourier spectra of the pressure and the volume flow velocities are presented since they reflect a direct measure of the muffling effect of the system. Figure 5 shows the pressure variation in the interior volumes described in Part I for the particular model which is used in this research. Figure 6 to Figure 10 show how the pressures change when the compressor is remodeled. It is useful for readers to compare each following graph to Figure 5 to see the effect of the design variations. We see that the gas pulsations presented in volume V 1 is "muffled" by the time we reach the last volume, V 3, as expected. Figure 6 shows the pressures in the interior shell volumes when the cross section area of the first neck, A 1, is changed. In the Helmholtz approach, the natural frequency of the first volumeneck combination following the valve can be written as (1) where cis speed of sound[ft/s], A is the cross section area of the neck[fe], Lis the length of the neck[ft] and V is volume of the resonator[ft 3 ]. As one can see in Eq.(l), the frequency of the gas pulsation in V 1 is increased when the cross-section area of the neck is increased, and vise versa. Because the muffling effect of the system arrangement is already sufficient, neither increasing the area A 1 by 50% nor reducing the area by 50% have much effect on the pressure variation at the exit volume V 3 Considering the structurally transmitted compressor noise, it 620

4 300 _-:::.-J 250 ~=l ~~--~----~ ,-, ~ ' ~ i 0 o.oo, ,.---, , "..... ~... - oos ---';..,.... ~ j!:. 0~ ~o:---~,~oc~,--~.~::----~,~~)~--~,~,o~--~"~"-,- f.t"' :~~.~"l ~'J ~ :o~;,:.::~l 2~----~""':-: :-:~~~-~ Ft~~i"" :;l"' iol'!,:e- (d~~loi!lo) Figure 1 Pres.s:ure in c:ylind~.:r and valve ~;over ford,= 0.01 and D: ~ 0.01 [lb sift] Figure 1 Pressure: in cylinder and v:!lve c:over ford,= 0.05 and D, s 0.05 [lb sift] Figure 3 Volume veloddes of gas plugs for o,,o, ~ o.oi(ibs/ft]:--. v,: ---. v,;----,v, 310,-----~ ~----~---~-.... H. :..001 / ' 0 ~ :..... :--_..ocao :r... ~..c::.:.: G:7.J ey.~ P.~ ort.ll,..~cf.;~~rt!'-!] : I :~:f::.:: ::: :: ::... :.:... i ::: ::. - -., [.., " :_ ~'=r :_::..., I,..... A 1 t:f _... ~~- -<JA :f :}! :t:!.ol ~~:- ~:::o ld:'i Fb:r.. Kn ~np'4l' f.::h!'r~t!~ 1JJ: -i ~ ~ :.... :...!.....::") &':!':J!l'lO P.:;;:~.: Qfl<V~gfei:Hr~~e! ;.... Figure 4 Volume velocities of g3s plu.s,s. for D,.D, = O.OS[Ibs!fi]:-. V,;- "", V::,V, Figure 5 Pr~ss:ure in interior volumes: -.~,; " -,P,;,P; Figure 6 Pressure in interior voh.1mes for 2A 1 : -. P,; ~-~ ~ Pz:..., Ps 315r----~ ~ , 31sr---~ ~---, 31C :; ;; ;, 31C ; ;. - los -~-: :~ ' -. ' " 295 _., ~ " ~ - ' ' :... JOS ;, I ;, - o ; ~ ,---.1., \ ;... :... l~---!... ~ ' ~\-', -...!.' '----~~:> --~,./ ~ ---' -;' ;. 2 a~e:----:=:!::----:,.;-::,o---~.-:::o,; ~,,------;;":;.:-t:c:., ~LQn<~~l~(~!:lr.f'-:!! Fig.ur=' 7 Pressor~ in interior volumes for O.SA1~ ~. P 1 ; ~&--, P::; -, PJ 2~!'1, - -~~ ~~......j~ J~ 0 2:l0.~~~~ {.0,:1 l;l:;t.:t 1Q.Jo] P.."'I~Q!'\ a~!~ (~r~j Figure 8 Pre.um:e in interior volumes for 2L 1: -,P,;----,Pz; --,1'; 2SS0!;------,: 2 >~J--,:!,:;---,.::,_,-:----::'.,::: 0 --,:-:~';:»,--I f:!':il!-on~ll:!(~rc"c"j Figure 9 Pressure in interior volum=s for 0.5Lt: -. P 1 ; ~~~-. P,;..., P, 621

5 " "'T"" ~.-----r--~---~ , ~,r-----~----~--~~ ; ~ -! , ' - '"' I ~---~ ----~ - --~-~ ~ ~:c ~":fj 600 ec:; 1;:..."\J Figur=: 10 Pressure in interior voi:jm~.s f'or SV 1: -.P,;--.P::.P, Figure II Fouri~r sp~.:tra or prc:is.!.!re i~ \alumes: -.P 1 : --.P::.P; Figure: ll fourier spectra of pressure in volumes for 2A1: -,P,: --,.P,::; -,P1,~,;------"'T"" , 170.,....-"::' \ -.. ~. -- "':... _--... ;...,.., -ec ', ,.,~o...L~--='.,::-----,,":"':-----,..,.,..., ,,.,...- j,.: ~ it~l"'c;y[1'1;:] ~o~-~~~--.-'oo,.,...---~~----~::--~,~ frcqyc.-q~r-1: ;.,,, -1co!:-,...L..--,:;_,::---.::c,::----,=,._...;.:.::;.'-=eoo; :j1:»:. ~~... ~rl~t;::) Figur~ l3 Fouri~r sp~c:tril of' pressure in volum S for 2L1: -,P,:---.P,:.P, Fig.ur~ l-4 Fourier spc=ctra of pressure in " otum~s for SVa: -.?,:---. P:: P; Figurl!' t S fourier sp-ectril of \'Olume vclo~ities: ~.V.;~:.V 1 :-.V:.: --.vl >0 '',; '!... \' :I ~\ \\ ;_ = ' ~-~<~~<... ; '... ~ :.... ~ - co;o...l--::r...,::---,,o::o---.""._.:.:..::..,a~'",--"",coo... rl..,l S' ~ ~ i ~ "' ""' ;-": (.. "" ;;(1 0 ~00 '"' " ftc'quiii!'i(:~{h::) W'l!.:.; 1CV:l -~r ,-----,_ ,.~ c: -!ia.:.._:_. < ~ \ ~.. -- ~..., _.,_:... :'-:: - I -, ~ ,_;... :... ~... _-_-'---..-,---., ?. -70.::-: ""..:-: -.. :... _ {.. : tio.9q ;-~:::.,,..- --,.,;-;----6();) '----IIW----',.:.; h~et\cy(h~j figure 16 Fouri~r spc=:ctra of\'oiumc!' \'docitil!'~ for 2..\ 1: --. Vo:...,\'a:... V,:: V1 Figure: 17 Fouri.:r spt!ctra of\ otumc \'elo~ities fo.r 2L 1: -. Vo: --r V,:--. \":::. V1 figure 1 s Fourie-r spectra or volume: 'Veloeitir:s for sv I: --. v,; ----, v,:- -. V:: "". v, 622

6 would be better to have no high frequency gas pulsation in volume V 1 However, it will cause unnecessary pressure rise if the cross-section of the neck, A~ois reduced too much(figure 7). Next we changed the length of the first neck, L 1 As expected from Eq.(l), the frequency of gas pulsation is decreased when the length of the neck is increased (Figure 8), and vise versa. When the length of the neck is decreased, more active gas pulsations and higher pressure rises occur(figure 9). This can possibly increase noise as well as interfere with the performance of the system. When the length of the neck is increased(figure 8), the pressure becomes more low frequency and the amplitude is reduced. This seems to be the better design as far as the noise is concerned. However, there is no significant effect on the pressure at the exit volume due to the variation of the length of the neck L 1 Thus flow transmitted noise into the condenser is not changed. Last, the volume of valve cover, Vh was increased to five times the original volume. Figure 10 shows that the frequency and amplitude of pulsation are reduced significantly. It can also be shown that the performance of the compressor improves when the valve cover volume is increased. However, there is a limitation to increasing the valve cover volume because of space restrictions in the actual compressor. Figure 11 shows the Fourier spectra of pressures in the three volumes of the gas passages. We can clearly see the strong influence of the oscillation of the valve cover. That the first volume and neck of the system dominates this frequency is demonstrated in Figure 12 where the neck area A 1 was doubled. Halfing this area seems to eliminate the resonance peak at the expense of a large pressure increase at the fundamental frequency, which would probably be undesirable from a performance viewpoint. Fourier spectra plots of pressures to go along with various other parameter changes discussed before are shown in Figures 13 and 14. It should be noticed that all Fourier plots were calculated using a record corresponding to the third period of the simulation, which was taken to be the period at which steady state had been reached. To estimate the insertion loss between different components of the system, it is often desirable to look at the Fourier spectra of the volume velocities in the various passages. This is shown in Figures 15 to 18. For example, Figure 15 corresponds to Figure 11. The volume velocity V 0 is the input from the discharge valve. Any subsequent volume velocity Fourier components which are larger than the V 0 components indicate that the system actually amplifies the oscillations coming from the valve. Note that the volume velocity is defined as where i ""' 0, 1, 2, 3. The subscript 0 indicates the valve location. (2) 3.2 Design of Modified Muffler System A extra volume with neck (a side branch Helmholtz resonator) is attached to the valve cover of the muffler system shown in Figure 11. This extra volume does not quite replace the side branch resonator located in the valve port, but can be viewed as an approximation. The actual configuration should be modeled eventually, however, by changing the way the flow passages of the valve are presently modeled; this can be done by considering unsteady flow effects. The frequency of the side branch Helmholtz resonator is tuned to three different levels, 450Hz, 600Hz, and 750Hz. In other words, the attached volume is selected so that the 623

7 frequency of the attached resonator becomes the desired value. The equation of natural frequency from Helmholtz resonator theory[l] is given by Eq.(l), with the subscript 1 replaced by 4. Figure 19 shows Fourier spectra of pressures in the interior volumes when the frequency of the side branch volume is tuned to 450Hz. It is seen that the amplitude of the pressure P 1 in the frequency range of 400Hz to 500Hz is noticeably decreased, compared to the standard model shown in Figure 11. This illustrates the filtering effect of the side branch resonator with a frequency of 450Hz. Figure 20 and 21 show the Fourier spectra of pressures when the frequency of the side branch resonator is set to 600Hz and 700Hz respectively. Figure 20 shows another strong effect of the side branch volume at the range of 5OOHz to 600Hz. The additional resonator to the valve cover was not shown to be very effective to reduce pressures in volumes V 2 and V 3. However, the pressure in the valve cover, which induces the driving forces of the pressure pulsation inside of the gas passages, was very well muffled. It can be concluded that the side branch resonator has a beneficial effect since it decreases the pressure pulsations in the valve cover. The effect of the side branch resonator is well observable in the frequency range of 400Hz to 600Hz. 175;---r ~--, 170; ~--., ,, ::.:.r.~\'l'''': ::.::_:l.::::: :: ; :.::..... ;.::\; :i<.~ j... ::.... ' : \ -\~ --~. ~ 1150 I ~. ; '... :... :... '... :::~ ~: "~ { >-~ ~... 1.CS :\ ,.. _.';" ~:~-.. \ - ;! 'q.: ~ ~\ : _;...! " L\ >f. I I- -- :... --,;;: -- : =-- i : \-... <;.. i:::-; ~ ;" --- :'"'"..:..,, '-'---,-' ,< 0 :-: : 6 :0: lrequ'!'i'!cfll-'l::j : 1 :-:-:.~---",;:.:-: u.o..,.. : ~.. :.. ::...., !----l--""' 2 ::: 0,----,.,:-:-, -~.-><>::---,,::::,-----:-!, 0 o-j lleq..tqft;y!hz! 140-1: !:-'----::,_C:-".< _.-----::'.,c:-, ~-~:--"':---:--.,.,..-, ~_j,t~~: lrc~.j~'l.,.j';i'i.;;j Fig.u... ~ 19 Fcurier spectra ofpl:'=s!iure for modified mufflc:r system v.ie.h 450Hz: ~. P1: ~---. P~;... PJ: ---- P11de Figure 20 Fourier speotra of pressure for modified JDuftlc:r system with 600Hz: -.. P,; - r-t P~:---. PJ:... t P,l4e Figure 21 Fourier spectra of pressure for modified muffl~r system with 750Hz; -,P.: --,P,:--.P;: ----.P,..., 624

8 4. CONCLUSIONS The research was focused on the simulation of the thermodynamic process in the compressor cylinder, the flow and dynamic response of the discharge valve, and the discharge gas pulsations with special attention to the design of mufflers. As a consequence of modeling these gas pulsations, it is now possible to evaluate various discharge gas muffler arrangements. The current model is already useful for the development of so called low pass filter mufflers. However, it is desirable to extend the predictive capabilities of the computer simulation of the rolling piston compressor to discharge gas pulsations of higher frequency ranges by considering resonances in the various gas passage and cavity elements and the discharge/condenser pipe. The motor gap between motor stator and rotor was modeled as a one dimensional plane wave element. Even though it is not clear at this point in time how important it is, it is desirable to model it as a cylindrical annulus of gas since higher order resonances could be predicted. The wave reflections caused by large volumes before and after the motor gap and before the discharge pipe exit were not predicted because of the Helmholtz simplification. Certain higher frequency components may be missing from the predicted spectrum in the current model. It is recommended to simulate the volumes before and after the motor gap as continuous systems with their own resonances. The anechoic termination assumption was applied to the modeling of the discharge pipe exiting the compressor and leading through the condenser to the expansion device. While this is still a reasonable approach, it is desirable to investigate this and model the discharge pipe/condenser pipe combination as finite with a typical distribution of quality of refrigerant gas. The influence of reflected waves from the condenser and expansion device can then be studied. The benefit of adding a side branch resonator near the discharge valve was also verified based on theoretical predictions. 5. ACKNOWLEDGEMENT The work reported in this paper was supported by Panasonic Industrial Company. 6. REFERENCES 1. Soedel, W., "Mechanics, Simulation and Design of Compressor Valves, Gas Passages and Pulsation Mufflers, "Short Course Notes, Purdue University, Kim, Y. K., "The Analysis and Simulation of Gas Pulsation in a Valve-Muffler system of a Rolling Piston Compressor," Master's Thesis, School of Mechanical Engineering, Purdue University, Kim, Y. K. and Soedel, W., "Theoretical Gas Pulsation in Discharge Passage of Rolling Piston Compressor, Part 1: Basic Model," Submitted to International Compressor Engineering Conference at Purdue,