CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 26, No. 1, 2013 ·61·
DOI: 10.3901/CJME.2013.01.061, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn
Real Gas Effects on Charging and Discharging Processes of High Pressure Pneumatics
LUO Yuxi1, 2, *, WANG Xuanyin1, and GE Yaozheng1 1 The State Key Lab of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China 2 School of Engineering, Sun Yat-sen University, Guangzhou 510006, China
Received December 19, 2011; revised March 5, 2012; accepted September 17, 2012
Abstract: The high pressure pneumatic system has been applied to special industries. It may cause errors when we analyze high pressure pneumatics under ideal gas assumption. However, the real gas effect on the performances of high pressure pneumatics is seldom investigated. In this paper, the real gas effects on air enthalpy and internal energy are estimated firstly to study the real gas effect on the energy conversion. Under ideal gas assumption, enthalpy and internal energy are solely related to air temperature. The estimation result indicates that the pressure enthalpy and pressure internal energy of real pneumatic air obviously decrease the values of enthalpy and internal energy for high pressure pneumatics, and the values of pressure enthalpy and pressure internal energy are close. Based on the relationship among pressure, enthalpy and internal energy, the real gas effects on charging and discharging processes of high pressure pneumatics are estimated, which indicates that the real gas effect accelerates the temperature and pressure decreasing rates during discharging process, and decelerates their increasing rates during charging process. According to the above analysis, and for the inconvenience in building the simulation model for real gas and the difficulty of measuring the detail thermal capacities of pneumatics, a method to compensate the real gas effect under ideal gas assumption is proposed by modulating the thermal capacity of the pneumatic container in simulation. The experiments of switching expansion reduction (SER) for high pressure pneumatics are used to verify this compensating method. SER includes the discharging process of supply tanks and the charging process of expansion tank. The simulated and experimental results of SER are highly consistent. The proposed compensation method provides a convenient way to obtain more realistic simulation results for high pressure pneumatics.
Key words: real gas effect, pneumatic simulation model, high pressure pneumatics
present, lumped parameters method is the main solution ∗ 1 Introduction method in the simulations for studying the dynamic characteristics[2–4]. Though there are many studies focus on The high pressure pneumatic system has been applied to the accurate formula derivation[5], the computation special industries, such as aeronautics, astronautics and the method[6–8] and the flow phenomenon[9–10] of real gases, in armament. Besides the merits of general pneumatics, the present, the computations and the conclusions in these high pressure compressed air has the advantages of high references are difficult to apply in the simulation for high power density, large distensibility, strong and burst pressure pneumatics. In actual practice, many detail force[1–2]. Many scholars have invited and done some conditions are unmeasurable. For example, it is hard and researches on the components and systems for high costly to get the accurate heat exchange areas and thermal pressure pneumatics[2–4]. However, most of these researches capacities of pneumatics. Meanwhile, there is no perfect are solely based on ideal gas assumption. The real gas heat exchange model in present. Heat exchange model is effect on the performances of high pressure pneumatics is still a research hotspot. Thus, the detail solutions for seldom investigated. The calculations of some simulation are usually hard to implement. The heat thermodynamic parameters are different for an ideal gas exchange conditions are usually revised by experiments. and for real gases[1], and it may cause errors when we The dynamic responses of most pneumatic systems and analyze high pressure pneumatics under ideal gas components are related to the changing and discharging assumption. processes of pneumatic containers. The real gas effects on In actual practice, the engineers pay close attention to the charging and discharging processes for high pressure pressure and response characteristics of the pneumatics. In pneumatics are studied in this paper. For the inconvenient in building the simulation model for real gas and the * Corresponding author. E-mail: [email protected] difficulty of measuring the detail thermal capacities of the This project is supported by National Natural Science Foundation of China (Grant No. 50575202) pneumatics, this paper proposes a method to compensate © Chinese Mechanical Engineering Society and Springer-Verlag Berlin Heidelberg 2013 the real gas effect under ideal gas assumption by
· · LUO Yuxi, et al: Real Gas Effects on Charging and Discharging Processes of High Pressure Pneumatics 62 modulating the thermal capacity of the pneumatic container v in simulation. In 2010, we have studied the real gas effects dhr cTpp ( , )d T v T d p , (3) T p on air exergy and throttle efficiency[1], the calculations of enthalpy, internal energy and the database of where p is pressure, v denotes the specific volume, and compressibility factors calculated by S-R-K equation are subscripts r and p denote the thermodynamic parameters of referred to Ref. [1]. The research object of this paper is the real gases and the isobaric condition, respectively. high pressure air at ambient temperature under 15 MPa. For enthalpy is a state function, the value of enthalpy is In this paper, the real gas effects on air enthalpy and irrelative with the integration path. This paper used the internal energy are estimated to study the real gas effect on same integration path as which used in the exergy the energy conversion. Based on the relationship among calculation of Ref. [1]. Enthalpy can be divided into two pressure, enthalpy and internal energy, the real gas effects contributions: the temperature enthalpy and pressure on charging and discharging processes of high pressure enthalpy[11]. Assuming the enthalpy of the initial state is pneumatics are studied. According to the above analysis, hT( , p ), the path is set to be: the gas firstly undergoes an and for the inconvenience in building the simulation model 00 isobaric process, in which the temperature changes from T for real gas and the difficulty of measuring the detail to T , and then the gas undergoes isothermal expansion at thermal capacities of pneumatics, we propose a method to 0 the temperature T , in which the pressure changes from p to compensate the real gas effect under ideal gas assumption 0 p . The enthalpy of hT(, p )can be calculated by the sum of by modulating the thermal capacity of the pneumatic 0 hT( , p ), the difference between hT(, p )and hT( , p ), and container in simulation. The experiments of switching 00 0 the difference between hT(,) p and hT( , p ). expansion reduction (SER) are used to verify this 0 00 Thus, hTpr (, )can be calculated by Eq. (4): compensating method.
Tp 0 v 2 Real Gas Effects on Enthalpy and Internal hTpr0(,) h cp ( T )d T v T d p , (4) Tp00 Energy T p
The dynamic performances of the pneumatics are related Employing the definition of compressibility factor Z, we to energy conversions. From Eq. (1) of the first law of can obtain thermodynamic[11], the energy conversion of the pv pneumatics is related to heat, work, air enthalpy exchanges, Z , (5) and air internal energy. The real gas effect influences the RT enthalpy and internal energy of air. where R denotes gas constant. 2 We can obtain the following expression: cf ddQ Wt h f gz ffd m 2 v R RZ 2 ZT . (6) c b Tpp p pT hb gz bbd m d, U (1) 2 For real gas, enthalpy can be calculated by where Q is the heat exchange, Wt is the technical work Tp2 exchange, h denotes the specific enthalpy, c denotes 0 TR Z hTpr0(,) h cp ( T )d T dp . (7) Tp velocity of air, g denotes the acceleration of gravity, z is the 00pT p height of air, m is the air mass, U denotes the internal energy of total air, subscripts f and b are the air inflation The environment model proposed by KAMEYAMA, et and deflation of the research object. al[14] was adopted to define the reference state; the reference temperature and pressure were 298 K and 101 2.1 Real gas effect on enthalpy kPa. The property of air at low pressure is close to ideal gas. Under ideal gas assumption, the specific enthalpy is We assumed that when the pressure is less than 101 kPa the calculated by Eq. (2), and the enthalpy is solely determined air is ideal gas. This paper does not consider high [11–13] by air temperature : temperature air, the cp of air is 1.004 kJ(kg • K) at the temperature 273 K, and is 1.006 kJ(kg • K) at the
hi cTp , (2) temperature 373 K. The isobaric specific capacity of air at the temperature 273 K is used in the following calculations. where cp is the isobaric specific capacity, T denotes the Thus, in this paper, the difference between enthalpies for absolute temperature, subscript i denotes the thermodynamic real gas and ideal gas is the pressure enthalpy of parameters of an ideal gas. p TR2 Z For real gas, the change of enthalpy can be expressed by dp . [11–12] 0 Eq. (3) : pT p
CHINESE JOURNAL OF MECHANICAL ENGINEERING ·63·
The pressure enthalpy is calculated from 101 kPa. This In this paper, the compressibility factors are expressed by study uses the same markers as Ref. [1]. The calculation of the functions of pressure and temperature, ZRT p is used
()ZTp in this paper is different from the to substitute v, Eq. (12) is changed to Joule-Thomson effect calculation of Ref. [1]. In ZRT Joule-Thomson effect calculation, the temperature of the T pT Z ZRT 0 p compressibility factors changes with pressure reduced. The ur0(,) Tv u cv ( T )d T ZRT d . T0 ZRT p ZT p pressure enthalpy is calculated under isothermal condition, 0 p the temperature of compressibility factors is the reference (13) temperature T0, which means ()ZTp is calculated by (ZZ298,pp 297, ) (298 297), the compressibility factors The reference state is 101 kPa, 298 K. The integration are calculated by S-R-K equation in this paper. begins with 101 kPa. The calculation of internal energy is related to the isovolumic path. In the calculation of Eq. (13),
2.2 Real gas effect on internal energy ()ZTZRT p is simplified to (ZT ).RT p For example, The real gas effect on internal energy is calculated by ()ZTZRT p for 101 kPa to 102 kPa is calculated by two methods for comparison. ZZ298,102 297, 297 102 298. For ZZ298,102 297, 297 102 298 is close to 1, which means the ratio of the compressibility factors of 2.2.1 Calculated by definition adjacent isovolumic condition is close to 1, the error of this Under ideal gas assumption, the specific internal energy simplification is very small. The value of Z297, 297 102 298 ui is calculated by Eq. (8), the internal energy is also is calculated by the interpolation of Z and Z . [11–12] 297,101 297,102 determined by air temperature : The integration step of dv is the volume change of 1 kPa. For example, for 101 kPa to 102 kPa, the integration step of ui cTv , (8) dv is
where cv denotes the isovolumic specific capacity. ZR298,102 298 ZR298,101 298 For real gas, the change of internal energy can be . 102 101 expressed by Eq. (9) [11–12]: 2.2.2 Based on enthalpy [11] p The relation between enthalpy and internal energy is dur cTvv ( , )d T T pd v , (9) T v h u pv. (14) where subscript v denotes the isovolumic condition. Similar as enthalpy, internal energy is also a state For ideal gas: function, it is assumed that the internal energy of the initial state is uT( , v ). The integration path is set to be: the gas 00 hii u RT. (15) firstly undergoes an isovolumic process, in which the temperature changes from T to T , and then the gas 0 For real gas: undergoes isothermal expansion at the temperature T , in 0 the isothermal expansion the volume changes from v to v0. h u ZRT. (16) The internal energy of uT(,) v can be calculated by the rr sum of uT(00 , v ), the difference between uT(,) v and The difference between real gas effects on enthalpy and uT(0 , v ), and the difference between uT(0 ,) v and uT(00 , v ). internal energy is (Z 1) RT . The pressure internal energy Thus, uTvr (,)can be calculated by Eq. (10): can be calculated by pressure enthalpy minus (Z 1) RT . Tv The compressibility factors at 298 K are used. 0 p ur0(,) Tv u cv ( T )d T T pd v . (10) Tv00T v 2.3 Pressure enthalpy and pressure internal energy of real pneumatic air We can obtain the expression from Eq. (5): The pressure enthalpy, the pressure internal energies which calculated by definition and based on enthalpy are p R RZ shown in Fig. 1. Some special values are shown in Table 1. ZT . (11) Tvv v vT From Fig. 1 and Table 1 the pressure enthalpy and pressure internal energy of real pneumatic air decrease the For real gas, internal energy can be calculated by values of enthalpy and internal energy. The real gas effects on enthalpy and internal energy of high pressure air are Tv2 0 TR Z larger than which of low pressure air. Under ideal gas ur0(,) Tv u cv ( T )d T dv . (12) Tv 00vT v assumption, at temperature 298 K, the enthalpy is 299.19
· · LUO Yuxi, et al: Real Gas Effects on Charging and Discharging Processes of High Pressure Pneumatics 64 kJkg, and the internal energy is 213.71 kJkg. Thus, the gas effects on charging and discharging processes for high real gas effects on enthalpy and internal energy are pressure pneumatics. innegligible for high pressure air. For the air less than 15 MPa, the values of pressure enthalpy and pressure internal 3.1 Steps for obtaining the pressure and temperature energy caused by real gas effect are close. It is because that characteristics the values of (Z 1) RT are small at 298 K. For example, In present, lumped parameters method is the main at 15 MPa, 298 K the compressibility factor is 1.023. The solution method in simulations for studying the dynamic real gas effect of hu at 15 MPa is only 1.97 kJkg. responses of the pneumatics, the following steps are usually used to obtain the pressure and temperature characteristics. Step 1: calculating the mass flow rates of orifices. The air velocity through an orifice is related to the energy equation (Bernoulli equation), isentropic condition, and the calculation of sonic velocity. The mass flow rate is obtained by air velocity multiply the air density and equivalent cross-sectional area. The current literature is lacks paper dealing with the mass flow rate of orifice for real gas. This paper uses AMEsim to calculate the mass flow rates of orifices in sections 3.2 and 3.3. The mass flow rate for real gas is related to the isentropic index k in AMEsim. For ideal gas, the mass flow rate through an orifice is calculated by Eq. (17): Fig. 1. Pressure enthalpy and pressure internal energy 21k kk Table 1. Pressure enthalpy and internal energy 2 kpLL p Apeff H , Parameter Value RTH k1 p HH p Pressure pMPa 1 5 10 15 p –1 q ppLH1.89 p L , (17) Pressure enthalpy h (kJ • kg ) 2.06 10.64 19.90 27.39 m Pressure internal energy (by 1 1.94 10.36 20.15 28.78 k1 definition) upd(kJ • kg–1) 22 k Apeff H , Pressure internal energy (based on k11 RTH k 1.93 10.37 20.30 29.36 enthalpy) upe(kJ • kg–1) ppHL1.89 , Relative difference compared with the Enthalpy 0.69 3.6 6.7 9.2 where q is air mass flow rate, A denotes the equivalent enthalpy and internal m eff Internal cross-sectional area of orifice, subscripts H and L denote energy at 298 K under 0.90 5.0 9.3 12.9 ideal gas assumption ∆% energy the parameters of high pressure and low pressure ends. Step 2: the internal energy of the air in the container can be calculated by Eq. (1). Combining with the air mass in
the container, the air temperature can be obtained. 3 Real Gas Effects on Charging and Step 3: the air pressure can be obtained by Eq. (18): Discharging Processes and the Compensating Method (18) pV ZmRT, When air flows from high pressure zone into low pressure zone in throttling, the temperature will change where V denotes the volume of the container. with pressure drops and this is referred to as the Work and heat exchanges are not considered in sections Joule-Thomson effect[1]. Joule-Thomson effect is a 3.2 and 3.3. The influences of gravity and air velocity in Eq. reflection of the real gas effect. Throttling is assumed to be (1) are ignored in this paper. For every special pneumatic, an isenthalpic process. Joule-Thomson effect can be the influence of real gas effect is different. This paper explained as the conversion between pressure enthalpy and provides an analysis method and estimates the real gas temperature enthalpy. effects on charging and discharging processes. The The dynamic responses of most pneumatic systems and simulations in sections 3.2 and 3.3 are carried out by components are related to changing and discharging AMEsim, and the simulation in section 3.4.2 is carried out processes of pneumatic containers. For example, a valve for by Matlab/Simulink. high pressure pneumatics usually uses a pilot valve to From the results of section 2.3, for the air at ambient adjust the pressure of pressure regulating chamber to temperature under 15 MPa, the enthalpy and internal realize the movement of main valve spool. The pressure energy of real air are less than which of ideal gas. The real variation of the regulating chamber is realized by charging gas effects on enthalpy and internal energy of high pressure and discharging processes[2–4]. This paper studied the real air are larger than which of low pressure air. The
CHINESE JOURNAL OF MECHANICAL ENGINEERING ·65· differences between real air and ideal gas for enthalpy and temperature decreasing rate in this simulation. Compared internal energy are similar. with this simulation, for an actual pneumatic which exists heat exchanges, the temperature decreasing rate is 3.2 Real gas effect on discharging process of constant relatively slower, the real gas effect on Eq. (18) is relatively volume container smaller. Fig. 2 and Table 2 are the simulation results comparison For a special pneumatic, the real gas effect is related to for the discharging process of a constant volume container the air mass in the container, air pressure and temperature, for real gas and ideal gas. The initial pressure and and heat exchanges. In general, for the same air mass temperature of the air in the container are 15 MPa and output of high pressure pneumatics, the real gas effect 293 K. accelerates the temperature and pressure decreasing rates during discharging process.
3.3 Real gas effect on charging process of constant volume container Fig. 3 and Table 3 are the simulation results comparison for the charging process of a constant volume container for real gas and ideal gas. The air is supplied by a constant temperature and pressure source of 15 MPa and 293 K.
Fig. 2. Discharging process of ideal gas and real air
Table 2. Comparison of discharging process of ideal gas and real air
Time Relative Parameter Ideal Real Difference ts difference ∆% Mass flow 15 650.7 631.0 19.7 3.0 rate 30 476.1 457.3 18.8 3.9 –1 qm(g • s ) 50 321.3 310.6 10.7 3.3 Air 15 262.1 256.4 5.7 2.2 Fig. 3. Charging process of ideal gas and real air temperature 30 235.5 227.4 8.1 3.7 TK 50 205.6 197.0 8.6 4.2 Table 3. Comparison of charging process of ideal gas Air 15 10.19 9.49 0.7 6.9 and real air pressure 30 7.06 6.35 0.71 10.1 Time Relative Parameter Ideal Real Difference pMPa 50 4.45 3.94 0.51 11.5 ts difference ∆% Mass flow 7 301.5 311.2 10.7 3.5 From the simulation results below, for the pressure rate 12 300.0 310.2 10.2 3.4 –1 characteristics of the discharging process of high pressure qm(g • s ) 20 187.1 171.2 16.1 8.6 Air 7 407.2 376.3 30.9 7.6 pneumatics, the real gas effect is innegligible. The reasons temperature 12 408.5 383.6 24.9 6.1 for the real gas effect: in AMEsim, the mass flow rate is T/K 20 409.1 392.1 17.0 4.2 related to the isentropic index k. In this simulation, the Air 7 5.07 4.84 0.23 4.5 difference is less than 4%, the mass flow of real gas is less pressure 12 8.62 8.52 0.1 1.2 than which of ideal gas. From the relation among pressure, pMPa 20 13.48 13.76 0.28 2.1 enthalpy and internal energy shown in section 2.3, combining with Eq. (1), for same air mass output of high For the influence of isentropic index k, in this simulation, pressure air, the temperature decrease is larger for real gas. before 16 s, the mass flow rate of real gas is larger than By Eq. (18), the air pressure can be obtained. For the air at which of ideal gas, the difference is less than 4%. For low temperature, and the pressure less than 15 MPa, the Joule-Thomson effect[1], the temperature of air flowing into compressibility factor is less than 1. Thus the real gas effect the container of real gas is less than which of ideal gas. on pressure decreasing rate is larger than which on From the relation among pressure, enthalpy and internal
· · LUO Yuxi, et al: Real Gas Effects on Charging and Discharging Processes of High Pressure Pneumatics 66 energy shown in section 2.3, combining with Eq. (1), for air container. For a discharging container, the temperature the same air mass input, the temperature increasing rate of of air in the container decreases, heat exchange makes the real gas is slower than which of ideal gas. For air at high temperature of the container decrease, and heat exchange temperature, the compressibility factor is larger than 1, decelerates the air temperature decreasing rate. From the combining with Eq. (18), the real gas effect on pressure is analysis of section 3.2, the real gas effect accelerates the air less than which on temperature, and the situation in which temperature decreasing rate. Thus, in simulation the real the pressure of real gas exceeds the pressure of ideal gas gas effect can be compensated by decreasing the thermal may exist. Similar as the discharging process, compared capacity of the air container. For a charging and with this simulation, for an actual pneumatic which exists discharging container, the real gas effect can be heat exchanges, the temperature increasing rate is relatively compensated by switching the thermal capacity of the container. By this method the real gas effect on step 2 of slower, the real gas effect on Eq. (18) is relatively smaller. section 3.1 can be compensated, the real gas effect on In general, for the same air mass input for high pressure Eq. (18) still exists. In actual practice, the real gas effect on pneumatics, the real gas effect decelerates the temperature Eq. (18) is relatively small. For example, in 20 experiments and pressure increasing rates during charging process. of following section 3.4.2, the maximum real gas effect on Eq. (18) occurred in situation Ⅳ, in the end of the 3.4 Compensation of real gas effect under ideal gas experiment, the pressure of PP1 and temperature of PT1 assumption were 8.94 MPa and 271 K, the compressibility factor was It is inconvenient for building the simulation model of 0.981 6. In other situations the real gas effects on Eq. (18) real gas. For real gas, different temperatures and pressures were less than 1%. correspond to different compressibility factors. Solving the For different pneumatic systems and different pressure corresponding transcendental equations of the compressibility ranges, the changes of the thermal capacitor values are factors from the P-R and S-R-K equations is required[1]. different. So the thermal capacitor values should be revised Even we have the database of compressibility factors, according to the experimental curves of the special iteration should be used to obtain the pressure and pneumatic system. Because the real gas effects of different temperature information. Thus, a method to compensate the real gas effect under ideal gas assumption is more pressure ranges are different, if the pressure span of the convenient. pneumatic system is large, to obtain more precise simulation results, different thermal capacitor values should 3.4.1 Methods be used for different pressure ranges. From Eq. (1), for the pneumatics, besides the exchanges of air enthalpy, the temperature and pressure characteristics 3.4.2 An example are also related to heat exchanges. In actual pneumatic In this section, an example for the compensating method systems, heat exchange conditions are usually revised by for a high pressure pneumatic is presented. Switching experiments. Thus the real gas effect can be compensated expansion reduction (SER) is a pressure reduction system by modulating the heat exchange conditions in simulation. for high pressure pneumatics. For high pressure pneumatics For a charging container, the temperature of air in the and electronic control systems, there is no mature throttle container increases, heat exchange makes the temperature valve in present. SER uses a switch valve to substitute the of the container increase, and heat exchange decelerates the throttle valve to realize pressure reduction. The air mass air temperature increasing rate. From the analysis of section flowing into the expansion tank is controlled by the on-off 3.3, the real gas effect decelerates the air temperature time of the switch valve, and the air pressure is reduced by increasing rate. Thus, in simulation the real gas effect can compressed air expanding in the expansion tank. The be compensated by increasing the thermal capacity of the experimental setup is shown in Fig. 4.
Fig. 4. Experimental equipment of SER 1. Pressure gauge; 2. Inlet choke; 3, 5. Flow control valves; 4. Outlet choke; PP1, PP2. Pressure sensors; PT1, PT2. Temperature sensors
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Supply tanks have been discharging during the whole process. The expansion tank was experiencing a charging process during the pressure raising period. We assumed heat exchanges occurred between the air in tanks and the corresponding environments (tanks). For the inside parts of the tanks were metal, and the outside parts were nearly adiabatic, it was assumed that heat exchanges caused the temperatures of tanks to change, and that these temperatures were the environmental temperatures of the air in tanks. The heat exchange model in AMEsim pneumatic library is relatively simple and it can not be modified, the compensating method is proved by the Matlab/Simulink under ideal gas assumption. Heat transfer coefficients are determined by the Ⅲ [15] Fig. 7. Pressure characteristics for situation equation of JIN, et al . The thermal capacities of tanks were revised by 20 experiments of different situations, which means the real gas effect has been considered in revising the thermal capacities. The initial pressures and temperatures are the same in the simulations and experiments. For the measurement of transient varying air temperature is a difficult issue, our primary concern is the pressure characteristics. The pressure characteristics of 4 situations are shown in Figs. 5–8, some simulation and experiment parameters and results are shown in Table 4.
Fig. 8. Pressure characteristics for situation Ⅳ
Table 4. Simulation and experiment parameters and results for 4 situations Situation Parameter Ⅰ Ⅱ Ⅲ Ⅳ
Initial supply pressure pi MPa 9.75 9.96 5.19 12.17 2 Area of outlet choke Ae mm 7.065 19.625 3.14 19.625 Output pressure Experiment 10 16 18 24
rising time tr s Simulation 9.6 14.5 17.8 23.8 Fig. 5. Pressure characteristics for situation Ⅰ Supply pressure Experiment 2.62 3.45 1.31 3.23 decrease ps,d MPa Simulation 2.59 3.33 1.32 3.11
Initial temperature of supply 286.4 284.8 296.8 283.3 tanks Ts,i K Initial temperature of expansion 277.8 276.1 289.3 279.6 tank Te,i K
The precisions of pressure sensors PP1 and PP2 are about 0.08 MPa and 0.01 MPa. PP1 could not be mounted before the inlet choke for safety, but the message of pressure sensor is recorded when the switch valve closed, PP1 can reflect the supply air pressure. For situation Ⅳ, the mass flow rate is large, the throttling effect of the switch valve is relatively small, it is hard to obtain the supply air pressure by PP1 during the process, but the pressure messages of the initial and end states can be used. Fig. 6. Pressure characteristics for situation Ⅱ From Figs. 5–8, after revising the thermal capacities, both
· · LUO Yuxi, et al: Real Gas Effects on Charging and Discharging Processes of High Pressure Pneumatics 68 for charging and discharging processes, the simulation Mathematical Analysis and Applications, 2002, 272(2): 507–535. model under ideal gas assumption reflects the actual [6] MONTARNAL P, SHU Chwang. Real gas computation using an energy relaxation method and high-order WENO schemes[R]. pressure characteristics of SER for high pressure NASA/CR-1998-208712, ICASE Report No. 98-42. pneumatics. Which means the compensating method is [7] GALLOUET T, HERARD J M, SEGUIN N. Some recent finite effective. volume schemes to compute Euler equations using real gas EOS[J]. International Journal for Numerical Methods in Fluids, 2002, 39(12): 4 Conclusions 1 073–1 138. [8] MOTTURA L, VIGEVANO L, ZACCANTI M. An evaluation of Roe’s scheme generalizations for equilibrium real gas flows[J]. (1) The pressure enthalpy and pressure internal energy Journal of Computational Physics, 1997, 138(2): 254–399. of real pneumatic air obviously decrease the values of [9] OKONG’O N, BELLAN J. Consistent boundary conditions for enthalpy and internal energy for high pressure pneumatics. multicomponent real gas mixtures based on characteristic waves[J]. The real gas effects on enthalpy and internal energy of Journal of Computational Physics, 2002, 176(2): 330–344. high pressure air are larger than which of low pressure air. [10] MALLINSON S G, GAI S L, MUDFORD N R. The interaction of a shock wave with a laminar boundary layer at a compression corner in For the air under 15 MPa, the values of pressure enthalpy high-enthalpy flows including real gas effects[J]. Journal of Fluid and pressure internal energy are similar. Compared with Mechanics, 1997, 342: 1–35. the enthalpy and internal energy of ideal gas at [11] BAEHR H D. Thermodynamics-An introduction to the fundamentals temperature 298 K, the relative differences of air at 10 and technical applications[M]. 5th ed. Berlin: Springer-Verlag, MPa are 6.7 % for enthalpy and 9.3 % for internal energy. 1981. (in German) (2) For high pressure pneumatics at ambient [12] WANG Baoguo, LIU Shuyan, WANG Weiguo. Aerodynamics[M]. Beijing: Beijing University of Technology Press, 2005. (in Chinese) temperature under 15 MPa, the real gas effect accelerates [13] Van WYLEN G J, SONNTAG R E. Fundamentals of classical the temperature and pressure decreasing rates during thermodynamics[M]. 3rd ed. New York: John Wiley & Sons Inc., discharging process, and decelerates their increasing rates 1985. during charging process. [14] KAMEYAMA H, YOSHIDA K, YAMAUCHI S, et al. Evaluation of (3) This paper proposes a method to compensate the reference exergies for the elements[J]. Appl Energy, 1982, 11(1): 69–83. real gas effect under ideal gas assumption by modulating [15] JIN Yingzi, LI Jun, BAO Gang, et al. The effect and determination of the thermal capacity of the pneumatic container in the overall coefficient of heat transfer in pneumatic charging and simulation. For a charging container, the real gas effect discharching system[J]. Journal of Harbin Institute of Technology, can be compensated by increasing the thermal capacity of 1998, 30 (1): 15–19. (in Chinese) the air container. For a discharging container, the real gas effect can be compensated by decreasing the thermal Biographical notes capacity of the air container. The experiments of SER LUO Yuxi, born in 1983, is currently a lecturer at School of support this compensating method. Engineering, Sun Yat-sen University, China. He received his PhD degree from The State Key Lab of Fluid Power Transmission and
Control, Zhejiang University, China, in 2011. His current research References interests include high-pressure pneumatic system and medical [1] LUO Yuxi, WANG Xuanyin. Exergy analysis on throttle reduction instruments and equipment. efficiency based on real gas equations[J]. Energy, 2010, 35(1): Tel: +86-571-87951271-6210, E-mail: [email protected] 181–187. [2] WANG Xuanyin, PI Yangjun, XU Zhipeng, et al. Principle and characteristics of on/off piloted pneumatic extra-high pressure WANG Xuanyin is currently a professor and a doctor supervisor at reducing valve[J]. Journal of Zhejiang University (Engineering The State Key Lab of Fluid Power Transmission and Control, Science), 2008, 42(6): 1 027–1 031. (in Chinese) Zhejiang University, China. He received his PhD degree from [3] WANG Xuanyin, CHEN Yize, LIU Rong, et al. Design and Harbin Institute of Technology, China, in 1995. His research simulation of pneumatic proportional extra-high pressure valve[J]. interests include fluid power transmission and control, intelligent Journal of Zhejiang University (Engineering Science), 2005, 39(5): machine and image information, etc 614–617. (in Chinese) Tel: +86-571-8793019, E-mail: [email protected] [4] YANG Gang, GUO Hao, LI Baoren. Dynamic simulation investigation of a novel high-pressure pneumatic proportional GE Yaozheng works at The State Key Lab of Fluid Power control valve[J]. China Mechanical Engineering, 2007, 18(12): Transmission and Control, Zhejiang University, China. He obtained 1 418–1 420. (in Chinese) his M.S. degree from Zhejiang University, China, in 2005. His [5] QIN Yuming. Exponential stability for a nonlinear research interests are mechatronics system and control engineering. one-dimensional heat-conductive viscous real gas[J]. Journal of E-mail: [email protected]