Purdue University
Purdue e-Pubs International Compressor Engineering Conference
School of Mechanical Engineering
1998
Theoretical Study of Design and Operating Parameters on the Reciprocating Compressor Performance S. Manepatil Indian Institute of Technology
G. S. Yadava Indian Institute of Technology
B. C. Nakra Indian Institute of Technology
Follow this and additional works at: http://docs.lib.purdue.edu/icec Manepatil, S.; Yadava, G. S.; and Nakra, B. C., "Theoretical Study of Design and Operating Parameters on the Reciprocating Compressor Performance" (1998). International Compressor Engineering Conference. Paper 1343. http://docs.lib.purdue.edu/icec/1343
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THEORETICAL STUDY OF DESIGN AND OPERATING PARAMETERS ON THE RECIPROCATING COMPRESSOR PERFORMANCE
Smita Manep atil, G.S. Yadava , B.C. Nakra Indust rial Tribolo gy, Machin~ Dynami cs and Mainte nance Engine ering Centre (ITMMEC), Indian Institu te of Techno logy, New Delhi-1 10016, India ABSTRACT
Mathem atical simula tion for the recipro cating compre ssor cycle incorp orating the effect s of common faults has been develo ped. The govern ing equatio ns for differe nt proces ses are derive d by using first law of thermo dynami cs, contin uity equatio n, equatio n of mass flow through valves , kinema tic equatio n for piston moveme nt and the cylind er heat transf er correl ations . This paper gives the results of theore tical study of effect s of design and operat ing parame ters on compre ssor perform ance. p B
y
A Ak
Cd cdf
De Fd Finit
h
Re m p k
NOMENCLATURE
density of air inside the cylind er square root of the ratio of orifice and flow area at inlet ratio of specif ic heats at consta nt pressu re and consta nt volume angula r veloci ty of crank shaft viscou s dampin g factor for valve spring s ana spring stiffne ss of valve valve discha rge coeffi cient drag coeffi cient of valve plate specif ic heat of air at consta nt volume equiva lent diamet er valve plate area on which the pressu re acts initia l force on valve plate instant aneous heat transf er coeffi cient Reynol ds number mass of air inside cylind er cylind er air pressu re therma l conduc tivity
Pr R n t T V ~
y
suffix c d e f s o p
w
821
of cylind er air Prandt l number spec ific gas consta nt ratio of connec ting rod length to crank radius time temper ature of air inside cylind er volume of cylind er air clearan ce volume valve lift cylind er discha rge equiva lent flow suction orifice piston wall
INTRODUCTION ing Most of the simu lation studi es on the recip rocatt of effec the e porat incor not do comp resso rs carri ed out to date leaki ng common fault s like leaki ng valve s, weak valve sprin gs, filte rs air ed clogg and pisto n rings , slipp ing belt drive s simu late [l,2] . A mathe matic al model has been devel oped [3] to effec ts of the ing porat the recip rocat ing comp resso r cycle incor with r resso comp ing common fault s for a singl e stage recip rocat on dent depen is ce disc type of valve s. The comp resso r perfo rman the on force the value s of the desig n param eters like initi al other valve disc, stiffn ess of the valve sprin gs and some valve and cons tants like drag coeff icien t of valve disc is also disch arge coeff icien t. In addit ion, the perfo rman ce eratu re. depen dent on opera ting param eter like sucti on air temp the These param eters are used in the input data for simu lating the on d depen ts resul uted comp comp resso r perfo rmanc e and the paper corre ctnes s of the chose n value s of these param eters . This t on effec their of study al gives the resul ts of the theo retic the comp resso r perfo rman ce. MODELLING OF COMPRESSOR THERMODYNAMIC CYCLE r Phys ical model of a singl e stage recip rocat ing comp resso The 2. and 1 es Figur and its therm odyna mic cycle are given in sion, equat ions gover ning the diffe rent proce sses of expan the ing apply by sucti on, comp ressio n and disch arge are deriv ed [4], s valve conti nuity equat ion, equat ion of mass flow throu gh trans fer first law of therm odyna mics, the cylin der heat ion of corre latio n, valve dynam ics equat ion and kinem atic equat The 1. e pisto n movem ent to the contr ol volum e shown in Figur gover ning equat ions used are as follo ws-
(1)
~
dmo =Cd. A
ctt
a
(2)
2p4P
1-P4
(3) h(t) De(t) '-"'0.05 3 (Re(t ) ]O.B[p r (t) ]0,6 k (t)
822
(4)
(5)
(6)
All these equations are solved using Runge-Kutta method. This simulation model can give cylinder air pressure, temperature, mass and valve displacement for the complete compressor cycle and also the harmonic components of pressure. It can predict the compressor performance giving the values of volumetric efficiency, volume flow rate and the performance ratio. STUDY OF PARAMETERS AFFECTING COMPRESSOR PERfORMANCE The compressor performance is dependent on the values of the design parameters like initial force on valve disc (F 1 nH), stiffness of valve spring (Ak) and some other constants like drag coefficient of the valve disc ( cdf) and valve discharge coefficient (Cd). In addition, the performance is also dependent on operating parameters like suction air temperature (Ts)• Some ot these design and operating parameters like F1 n1 t , Ak and Ts may vary in practice in due course of time. The study of the effect of the variation of each of the above parameters has been carried out by assigning different values to each of these parameters individually in the known range while keepinq the others as constant for a fixed discharge pressure.
The initial force [ F ,inJ:t.J depends upon the stiffness and the initial compression of the spring. To study the effect of F J.nit on suction valve plate, the values in the range of 7 to 47 N were assigned and the compressor performance was computed.The cylinder air pressure, temperature and mass time diagrams are shown in Figures 3,4 and 5 respectively . With the increase in FJ.l\it the suction and discharge processes are delayed. The compression process begins at a little lower pressure and the maximum cylinder air pressure increases. The mass of air inside the cylinder decreases with increase in F 1 nit• The cylinder air temperature is not much affected. The instantaneou s valve displacement for different values of F init are given in Figure 6. It has been observed that the suction and discharge valves open for shorter duration as F init increases. The performance parameters are given in Table 1. The mean cylinder pressure, volume flow rate, volumetric efficiency and performance ratio decrease with the increasing values of F 1 nn• The cylinder air pressure harmonics for different values of F1 n1 t are given in Table 2, which indicate a prominent increase in 4th and 12th harmonic. Similar study on F 1 n 1 t , range 25-100 N, for discharge valve plate indicates that its increase leads to the shifting of
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compres sion and discharg e curves of the pressure -time diagram towards the right hand side. The performa nce paramet ers are not affected signific antly. The 1st, 2nd, Jrd, 4th and lOth pressure harmoni cs show an increasi ng trend and 6th harmonic shows a decreas ing trend with the increase in F1.,u.. '
The study on spring stiffnes s [AkJ of suction valve, range 0.45-18 kN/m, indicate s no signific ant variatio n in the cylinde r air pressure and tempera ture-tim e diagram s. The duration of suction valve opening is minimum for an optimum value of Ak and increase s for the other values. The performa nce paramet ers have optimum values correspo nding to a particu lar value of Ak causing suction valve closure at BDC. For other values the performa nce paramet ers show a decreas ing trend. The Jrd, 5th, 9th pressure harmoni cs show an increasi ng trend and 7th, 8th harmoni cs show a decreas ing trend for increasi ng values of Ak. In case of discharg e valve, (range 10-45 kN/m), weak spring shows lower pressure during the discharg e process and complete closure. of discharg e valve at the end of the cycle. The variatio ns in the magnitu de of valve lift are also reduced . With the increase in Ak a slight decrease in the performa nce ratio has been observed . The 1st, 2nd, 3rd, 4th, 5th, 9th and lOth pressure harmoni cs show an increasi ng trend whereas 6th, 11th and 12th harmoni cs show a decreas ing trend with the increasi ng Ak. The study on suction air tempera ture [Ts] in the range 20450C shows that cylinde r air tempera ture decrease s and mass of cylinde r air increase s with decrease in its value. The perform ance paramet ers decrease with the increase in Ts• The study on drag coeffic ient of valve disc [Cd~], in the range 0.25-0.4 0, shows that increase in its value shifts the compres sion curve of the cylinde r air pressure -time diagram towards left hand side. The maximum cylinde r pressure and the fluctuat ions of pressure during the discharg e process are reduced with the increase d value of eM. The duration s of opening of suction and discharg e valves also increase with the increasi ng Cdf" The performa nce paramet ers increase with the increasi ng values of Cdf" The 1st, 2nd, 7th, lOth, 11th and 12th pressure harmoni cs show an increasi ng trend while, 3rd, 4th, 5th, 6th, 8th and 9th harmoni cs show a decreasi ng trend with the increasi ng values of C 11~ The study on the discharg e coeffic ient [Cd] in the range 0. 5-0. 9 shows that increase in its value indicate s increase d fluctuat ions in the cylinde r air pressure during the discharg e process . The duration of suction valve opening is minimum for a particu lar value of the cd and increase s for all other values of cd. Other perform ance paramet ers have maximum values for the particu lar value of cd and decrease for all other values. The 5th pressure harmoni c increase s whereas the 2nd and 3rd harmoni cs decrease with the increase in the value of cd.
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CONCLUSIONS The computed results in the simulation program depend on the design parameters like Finit and Ak. Some other constants like cd and Cdf affect the compressor performance significantly and hence it is important to choose these parameters carefully in pr'actice for getting meaningful results. The performance is also dependent on operating parameter like Ts. 1.
2.
3. 4.
REFERENCES Benson, R. S and Ucer, A. s., "A Theoretical and Experimental Investigation of a Gas Dynamic Model for a Single Stage Reciprocatin g Compressor with Intake and Deli very Pipe systems", J. Mech. Engg. sc., v. 14, No. 4, 1972, 264-279. Prakash, R. and Singh, R., " Mathematical Modelling and simulation of Refrigeratin g compressors" , Proceedings of Compressor Technology Conference, Purdue University, 1974 274-283. Manepatil Smita, "Simulation and Condition Monitoring studies on Reciprocatin g Compressor", Ph.D. thesis, Indian Institute of Technology, Delhi, 1996. Schwerzler, D. D. and Hamil ton, J. F. , "An Analytical Method for Determining Effective Flow and Force Areas for Refrigeratio n compressor Valving Systems", Proc. camp. Tech. cont., Purdue University, 1972, 30-36. Table 1. Performance parameters for different values of Initial force on suction valve plate. Performance parameters
Initial force on suction valve plate, (N)
17
7
Mean .cylinder pressure(Pa) Volume flow rate (scfm) Volumetric efficiency (%) Performance ratio (kg/J)
5
5
1.89 X 10 25 81.7 4.66 X 10- 6
1.85 X 10 24 78.9 4.60 X 10-6
27
47
1. 77 X 105
1.63 18 60.1 3.96
22 72.5 4.39 X W 6
X 10 5
X W6
Table 2. Amplitude of cylinder air pressure harmonics for different values of initial force on suction valve plate(Pa). Harmonics
1 2 3
4 5 6
7 8 9
10 11 12
Initial force on suction valve plate, (N) 7
17
27
47
167615
16880-3 110343
167285 110856 63818 28185 10394 13396 16'508 18989 12085
163830 112550 67057 34911 10901 10409 19418 16775 9942
3794
4277 1474 1953
110346
60054 24751 9102 13961 19808 17140 9557 3316 4715 6091
61327
25687 10001 14962
17025 18587 10898 3659 4439 5714
825
2837 4400
Dlschorg~ charnbel"
Sud'u~m chamber
4
P
"'
~400"
'j!130o
0. ·i§ 300 :;;
"'c. E
~200
~200
iS 100
100
0 0.01
0.02
0.03
0.04
0.011
0.0!1
0.07
O.OB
o.oo
o.03
0.02
o.o1
o.os
o.os
o.04
o.oa
o.01
Time. sec.
Time, sec.
Fig.4 Cylinder air temperature diagram for different values of Finit on suction valve
Fig.3 Cylinder air pressure time diagram for different values of Finit on suction valve.
1 . 4 - , - - - - - - - - - - - . , - - - - - - - - - - - - -..... -7N ··17N -271'1 -47N
E
E
E
"'1.0 IIi
"i
~o.G
"'OJ E
.,u
·~o.e
'5.
"'
"' "' 0.500 ]!_
'Cl
'6
~04
?;'
~
M!
0.01
0.02
0.03
0.04
o.os
0.08
0.07
0.01
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Time, sec.
Time, sec.
Fig.6 Cylinder air mass-time diagram for different values of Finit on suction valve.
Fig.5 Valve displace ment-tim e diagram for different values of Finit on suction valve.
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0.08
