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International Compressor Engineering Conference School of Mechanical Engineering

1974 Computer Simulation of Valve Dynamics as an Aid to Design A. M. Bredesen University of Trondheim

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Bredesen, A. M., "Computer Simulation of Valve Dynamics as an Aid to Design" (1974). International Compressor Engineering Conference. Paper 117. https://docs.lib.purdue.edu/icec/117

This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional 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.html COMPUTER SIMULATION OF VALVE DYNAMICS AS AN AID TO DESIGN

Arne M. Bredesen, Scientific Assistant, Div. of Refr. Eng., Norwegian Inst. of Technology

INTRODUCTION appear in Fig. 2. The transducers were calibrated statically before installation. The paper presents some results from a re­ In order to make it possible to search work carried out at the Division check the of calibration during operation, thin Refrigeration Engineering at the Norwegian hori­ zontal electrodes were installed at Institute of Technology under the guidance defin­ ite levels. This arrangement is also of professor G. Lorentzen. The purpose of the shown in Fig. 2 (3). When the valve plate project was primarily to develop a passes computer the electrode, a sharp capacity simulation model for calculating signal the valve peak is produced. When the signals behaviour under operating condi­ from tions, the two types of pick-ups are record­ taking into consideration the pres­ ed together, sure pulsations it is possible to fix the in suction and discharge. necessary calibration The computer model may be level, as shown by applied in many an example in Fig. 3. ways. Simulated test runs of a proposed valve design can be arranged in short time. The pressure pulsations were indicated It is also possible to use the.model to by develop means of piezoelectric transducers. Fig. simple design rules, so that opti­ 4 shows mal valve a cross section of the pick-up-­ designs can be approached by which simple calculation. was used to calibrate the pressure signal. A small plate (A) is balanced between The work the system pressure Pl and the was primarily concentrated on constant ring-plate valves, calibration pressure pz. When­ but the results may be ever the pressure applied to other designs. difference across the plate is turning, the plate starts to move from one seat COMPUTER MODEL DEVELOPMENT to the other. Again the ca­ pacitive effect is used to indicate this motion. Experimental Works The delay due to inertia is small, as evidenced by the sample recording in Fig. 5. The computer model has to be calibrated by comparing the calculated behaviour with During the measurements on experiments the compressor was real valves under normal working with operation. The major air in an open system. The aim of the measure­ plant allowed continuous ments is to find the relation variation of com­ between pressor speed and pressures. forces and valve reaction. The gas flow The tempera­ tures and static pressures throughout through the valve produces a force which the system, together with the compressor determines the valve movement together with pump­ the spring ing capacity and energy consumption, were forces and other minor effects determined (friction, oil sticking by standard methods. The valve etc.). The gas and pressure oscillations were force depends on the pressure recorded by difference an UV-recorder. The recordings were across the valve and the flow dig­ conditions. italized and fed into a computer. Process It is therefore necessary to indicate the pressure diagrams could be drawn to any desired oscillations on both sides toget­ scale her with by means of an automatic drawing ma­ the valve movement. It is desir­ chine. able to be able to calibrate the measuring equipment during operation to eliminate the Test series were run possible influence of on two different temperature and oil valves. Fig. 6 demonstrates content on the transducer characteristics. a typical re­ sult from the first one. The installed springs were too strong, choking An experimental discharge valve with the gas the force, so that the valve could not necessary electronic equipment was develop­ open ed and completely. It oscillated heavily, bounc­ installed in a single-cylinder com­ ing pressor back on the valve seat several times of the uniflow type, Fi~. 1. The during the opening period. The mechanical valve lift is indicated in three points strain on the valve plate was increased, around the pheriphery in order to discover and such oscillations should be avoided. any tilting. Capacitance transducers were used and the dimensions of the electrodes When the valve was operated without springs

171 in the second series, it behaved more fav­ to oil sticktion at the boundaries is tak­ ourably from a mechanical point of view, as en into account, and so is the reflection can be seen in Fig. 7. However, the valve when the valve plate hits the seat or the closing was delayed, and this caused blow­ stop. back and reduced volumetric efficiency. This was confirmed by the direct capacity The main purpose of the discharge line mo­ measurements. del is to yield the pressure Pdr needed in eq. 2. This pressure depends on the mass Computer Model entering the discharge line through the valve and the pressure pulsations which The simulation model requires mathematical are reflected from the open end. The dis­ expressions for the physical processes go­ charge line process was calculated by a ing on in the compressor. For the mathe­ method of characteristics, described by matical treatment the system was divided Benson [1]. In the case of the test valve into three separate parts, mutually ex­ the gas was flowing directly into the dis­ changing mass and energy. In the case of charge line and produced a known particle the discharge valve these are the cylinder, velocity, which is used as boundary condi­ valve and discharge line system. The con­ tion at the valve end of the line. At the nections between the systems are visualized other end the pressure is assumed to be in the schematic block diagram of Fig. 8. constant.

The cylinder process is described by the The result of the mathematical deductions equation: is a system of simultaneous differential equations. These can be solved by step­ dp wise integration, using the Kutta-Merson c = K numeric method with adjustable integration steplength. The typical CPU-time needed for a complete simulation of two revolut­ The cylinder volume Vc and its variation ions on the UNIVAC-1108 computer was 40-50 dVc are known functions of the crank angle s. The computed process is presented as e. The mass leaving the cylinder is calcu­ tables and drawings, allowing easy compari­ lated by the formula: son with the measured results. The comput­ er also calculates the mass delivered by the compressor and the valve energy losses aAo / d8 - -.h. 2p (p -p ) . - during one revolution. h c c d w 0 By the calibration good agreement between The flow coefficient a is known from static measured and calculated process was attain­ measurements on the test valve. ed, both for valve behaviour and pressure oscillations. This can be seen from Figs. When the valve plate moves between the 9 and 10, giving some typical results~ stops, the behaviour can be described by was found that the gas and spring forces the simple dynamic equation, assuming one are the most important ones. The other degree of freedom, which was confirmed by influences may be neglected without any the experiments: great error, at least for the valve type used in this project. The valve reflection at the seat was found to be very low (CRefl = 0.01). At the stop the reflection depends on the actual geometry. When dis­ tance pins are used to reduce the maximum All the forces which could possibly affect lift, a reflection coefficient in the order the valve behaviour, have to be included of 0.4 was found. and evaluated. The main forces are the following: A similar model was developed for the suc­ tion valve system, applying the experience Gas force C ·A • (p -p ) gained in analysing the discharge. d v c d Spring force: F +C "h COMPUTER MODEL APPLICATION so s Dynamic Design The drag coefficient and spring character­ istic are found by static measurements on As a result of the experiments the need for the valve. Additionally the model includes more adequate spring design rules was re­ the forces caused by damping, friction and cognized. The simulations show that it is gravity. The mathematical description of the balance between gas force and spring these forces is omitted here, but they force which mainly determines the valve be­ include unknown °Constants" which have to haviour. The gas force variation is to be found by the calibration of the model. some extent fixed in a specified compressor process, and the problem The effect of opening and closing delay due of choosing the

172 appropriate springs remains. They should ing conditions, good valve be sufficiently behaviour is weak so that the gas force maintained. Too low compressor can hold the valve speeds may fully open. When the lead to increased volumetric losses. gas force decreases towards the end of the stroke, the springs should close the valve Other details may also be important to the without oscillations and in time to avoid dynamic behaviour blow-back. of the valve. When the That means that the valve discharge or suction chamber should close volume is exactly at pressure equalizat­ small, the pressure pulsations ion between may affect cylinder and suction or dis­ the valve operation. This charge. is demonstrated by the simulation run in Fig. 14. A sud­ den pressure decrease reaches Based on the the valve at experiences from computer mo­ the moment of closing, causing del simulations an extra a simplified equation for valve opening and blow-back, the valve closing with reduced process was designed. volumetric efficiency (10 percent This could loss). be solved to give a simple equ­ This problem could be corrected ation for calculating by adjust­ the optimal spring ing the discharge line length to omit stiffness. The sud­ solution is based on the den pressure increase or decrease assumptions that at the no oil sticktion occurs, dead center, Fig. 15. Consequently and that the springs the have no initial force pipe line length has to be considered (Fso = 0). The solution in may be described special cases. By the simulation shown by the following dimensionless in formulaes: Fig. 15 an extra volumetric gain of about 3 percent was achieved as a result of the Discharge valve: 53 B"*"" 3.22·A~· extra draining of the cylinder by low dis­ charge pressure at the time of valve Suction valve 51 clos­ B>~< 2.16 ·A~· ure. The effect may be utilized intent­ ionally both for the suction and discharge A ·r 2 l ( cyl system to gain marginal volumetric improve­ A*- 2 · cd · aA ment. 0 With the developed equations ·w 2 it should be s possible to design the valves to function 7 properly for a given compressor under spe­ cified working conditions. In special cases, where for instance the pipe-line ® pressure pulsations might affect the valve process, the computer model has to be used. When the geometry and working conditions However, the design formulae will be of are given, together with the drag coeffici­ benefit even here, giving optimal valve de­ ent (Cd) and flow coefficient (a) of the signs with less simulation runs, thereby valve, the dimensionless drag force A* may saving expensive computer runtime. be evaluated. The dimensionless spring force B* and the optimal spring stiffness REFERENCES Cs can then be calculated from the equat­ ions given. [D Benson, R.S. and Oger, A.S.: "An Approximate Solution for Non­ The design system was tested on the comput­ steady Flows in Ducts with Friction". er models. When the proposed springs were Int. Journal Mech. Science, vol. 13, used, satisfactory valve behaviour was ob­ 1971, pp. 819-824. tained, as evidenced by the simulation ex­ amples given in Figs. 11 and 12. For the [~ Bredesen, A.M.: suction valve delayed pressure equalization "Unders¢kelse av ventilenes bevegelse could occur and result in valve malfunct­ i stempelkompressorer". ioning. The simulation in Fig. 12 shows ("Investigation of the valve behavi- that this problem is handled automatically. our in piston compressors"). The design formulae were also used to cal­ Thesis for the technical licentiate culate new springs for the discharge test degree at the Norwegian Institute of valve, and good operation was obtained, Technology, 1973, 319 pages in Norweg­ Fig. 13. ian. LIST The equations were based on the assumption OF SYMBOLS of zero initial spring force. However, si­ A - maximum valve mulations indicate that initial spring 0 flow area force may be used without affecting the A - valve plate front area valve behaviour much. But then the spring v A - constant must be adjusted, so that the max­ cyl cylinder cross section imum spring force at the valve stop is not Aw. - dimensionless gas force changed. When the valve is operated not (defined in text) too far from the originally specified work-

173 - dimensionless spring force (defined in text) cd - drag coefficient cs - spring stiffness N/m F - force acting on the valve N v F - gas force N g F - spring force N s F - initial spring force N so h - valve lift m ho - maximum valve lift m m - mass content of cylinder kg / c .'// m valve plate mass /. / v kg n - compressor speed rpm

- cylinder p~essure bar - discharge line pressure bar - crank radius v - cylinder volume c a - flow coefficient e - crank angle rad Fig. 1 Test valve with instrumentation K - adiabatic exponent 1 Valve plate - density of cylinder gas kg/m 3 2 Piezoelectric pressure trans­ ducers - compressor angular velocity rad/s 3 Pressure calibration pick-up - resonance angular velocity 4 Capacitance valve displacement of spring system rad/s transducer 5 Valve displacement calibration pick-up

~--- I -

LD.C UD.C

Fig. 2 Displacement transducer arrangement 1 Valve plate 2 Capacitance displacement trans­ Fig. 3 Calibration of valve lift signal ducer 3 Calibration electrodes

174 L.D.C U.D.C

Fig. 4 Pressure calibration pick-up Fig. 5 Calibration of signal from the cyl­ inder pressure transducer

-;~[ff\FiiJ I I BAR ;,o -~Et12EJ ~-o- _r-· ·--,------...,.o - I ·-- Pd r----· -- .. ~

1\ v . ·-- } f-- ...... -- ~ ·--r--- I "1'0.0 . __ j___j

Fig. 6 Typical experimental result. Fig. 7 Typical experimental result. Discharge valve operated with Discharge valve operated without springs (Fs ~12 N, Cs=ll400 0 N/m). springs. Compressor speed Compressor speed 400 rpm. 400 rpm.

Spring force

Fig. 8 Schematic block-diagram of discharge valve process

175 M'1 2.00 I II ~-50 I h I ~.QD I

I \./ D.DD

BAR 3.0

2.0

l..D

Q.D D.O E;D.D l.20.0 ~ao.o 2.roo :"!!XJ.O DEG. -.-- SJ,mulotJqn --- -Experim,.nt

~F~i~g~·~~g Comparison of experiments and computer simula­ tion fo;r? discharge valve operated with springs. Compressor speed 400 rpm.

I~J'• 0.75 \ I , I 0;50 ' I I 0.25 -~ ---·-- I I 0.00

.------,------.------.------.---· -~----··. -

2.0 ~~~,--~~~~--~~~~p~d-~~~~-£:/~~?~~-4-~---- \ __ _;;;.::; .1,.0 t---\===f=====l====~;;l=..,:;;..::;..~--j-----+---,-- ~--- --c------PC

00 DO 500 :l.ZDD :l.BOO z.o~oo :'!DO.D :'!500 DEG. -- Sirnulot1on ~---Exp~rim~nt

Fig. 10 Compqrison of experiments and computer simula­ tion for discharge valve operated without springs. Compressor speed BOO rpm.

176 "">OO .----.---,.~---,----.~.-~~~ ··~--+- -J ! - ' -r--- T --~ l---- -~ ' ' ---,------,---,------, --- _L- --+------r+-----1

~ig. ll Computer simulation of a discharge Fig. 12 Computer simulation valve process. of a suction Valve springs de­ valve process. Valve signed according springs de­ to eqs. 4 and 5. signed according to eqs. Compressor speed 4 and 5. 600 rpm. Compressor speed 1450 rpm.

Fig. 13 Experiment recording of discharge Fig. 14 Computer simulation demonstrating test valve fitted with springs possible calculated influence of discharge by eqs. 4 and 5. line Cs pressure oscillations on the = 6000 Njm. Compressor speed valve 850 rpm. behaviour. Discharge line length 1.38 m. Camp. sp. 1450 rpm.

Fig. 15 Same as fig. 14, but the discharge line length has been adjusted to 0.92 m.

177