Thermal-hydraulic Modeling and Simulation of Piston Pump

Transcription

1 Vol.9 No.4 CHINESE JOURNL OF ERONUICS Noveber 2006 heral-hydraulic Modelg and Siulation of Piston Pu LI Cheng-gong, JIO Zong-xia (School of utoatic Science and Electrical Engeerg, Beijg University of eronautics and stronautics, Beijg 00083, Cha) bstract his aer resents a kd of odelg aroach to the study of the theral-hydraulic iston u hich is used the airlane corehensively. set of lued araeter atheatical odels are develoed hich are based on conservation of energy. Heat transfer analysis for the iston u is also given the aer hich the heat flo side the iston u is described recisely. he theoretical basis and odelg strategy are alied a tyical theral-hydraulic circuit contag the iston u. Siulation results are resented hich sho a coarison of odel/rig erforance and the agreeent obtaed deonstrates the validity of the odelg aroach. Key ords theral-hydraulic iston u teerature odellg (4): (2006) V233.9 H37 K2 In hydraulic systes of an airlane, the oil teerature aly deends on the efficiency of soe orkg coonents, such as iston us, otors and valves. Often the iston u is the a coonent hydraulic oer sources. s the develog of airborne hydraulic syste, the ut ressure and oer of the iston u are higher then ever. High ut ressure and oer ill lead to larger oer losses hich can ake the oil teerature becoe undesirably high. highly elevated oil teerature can brg any robles to hydraulic systes and even ake the syste can not ork roerly. herefore, it is necessary to ake theral hydraulic odel of the iston u and redict the teerature changes across the iston u the design rocess of the hydraulic oer syste. Interest the theral consideration of iston u has surfaced through years. In 989, Kjølle [] studied therodynaic efficiency ethods for us. In Norgard [2] (973) and Dorey and Harris [3] (989) teerature calculations for us ere discussed. hese researches ade it ossible to redict the fluid teeratures of the theral-hydraulic iston u the designg rocess. But these aers are aly focus on the steady-state theral calculation of the iston u hich can not give the therodynaic odel of the u detail. In this aer, a generic and accurate theral odel of the iston u is troduced and heat transfer analysis of the u is resented. t the end of this ork, the validity of the odelg aroach is deonstrated by a coarison of odel/rig erforance of a hydraulic circuit cludg the iston u. Received date: ; Revision received date: Foundation ite: National 863 Project of cha

2 Neveber 2006 heral-hydraulic Modelg and Siulation of Piston Pu 355 Basic Modellg Method he conservation equation for energy is the basic equation for theral-hydraulic odelg. For lued-araeter odels and one-diensional flo, there is a silified reresentation of this equation. he basic relationshi for the theral change of the fluid over a hydraulic iston u is the first la of therodynaics alied to a flo rocess of the fluid volue [4]. he fluid volue is shon Fig.. For a colete and ore corehensive atheatical survey, see Refs. [5] and [6]. Fig. Control volue he corresondg ordary differential equation for fluid energy a volue V is = h h + E () here W is rate of ork excet the ork required to ush ass to and of the control volue hich is taken care of by usg enthalies for the energy of fluid streas. he energy E the control volue is the su of the ternal energy U, the ketic energy KE and the otential energy PE E=U+KE+PE. If the ketic and otential energy are neglected, the tie rate of change of the energy can be exressed accordg to Eq.(2), de d( u) du d = = + u (2) Sce the fluids this study do not change hase, the secific enthaly can be exressed as a function of teerature and ressure, that is h=h(, ). So the tie derivative of h can be exressed as dh d d = + (3) he first ter Eq.(3) is recognized as the secific heat at constant ressure c, c = (4) he second ter deands soe rearrangg usg the so-called ds equations [6]. It can be exressed as Eq.(5), here v is the secific volue, v = v = v vα (5) Eq.(3) can be reritten as Eq.(6) by Eqs.(4) and (5). dh d d = c + ( α ) v (6) he secific enthaly is defed as H=u+v (7) Introducg Eqs.(6) and (7) Eq.(2), Eq.(8) is obtaed, de d d d dv = c α v + h (8) he contuity equation for one-diensional flo gives d = (9) Cobg Eqs.(8), (9), (0) gives d = [ ( h h) + ( h h ) + c (0) dv d + + α v In ost theral-hydraulic coonents, W reresents the rates of boundary shaft and ork ork. It can be ritten as W = W s + W b () W b is the rate of boundary ork. It is calculated by V W d b = (2) Introducg Eqs. () and (2) to Eq. (0) gives d = [ ( h h) + ( h h ) + c (3) d s + α V If it is assued that the average enthaly ith the control volue equates to the leavg enthaly regardless of the let conditions [7], Eq.(3) can be exressed as d d = ( h h) + Ws + α V (4) c he change secific enthaly ith the control volue is related to the change ressure and teerature by h h = c ) + ( α ) v( ) (5) ( Eq.(5) has been derived by tegratg fundaen-

3 356 LI Cheng-gong, JIO Zong-xia CJ tal relationshis beteen enthaly, ressure and teerature [7] and all fluid araeters are relaced ith their ean values over the teerature and ressure range considered (dicated by barred notations). Eq.(3) or Eq.(4) is lued araeter equation reresentg conservation of energy. 2 Heat ransfer nalysis Usually, the variable dislaceent iston u is used the airlane. But the heat transfers beteen the variable and fixed iston u are alost the sae. So the scheatic for the fixed dislaceent axial iston u is reresented Fig.2 hich is ore tuitionistic than that for the variable iston u. here are three fluid chabers the u. Fig.2 Fixed dislaceent axial iston u he odel of theral-hydraulic iston u consists of four nodes: three fluid nodes and a ass node(fig.3). he let fluid node reresents the fluid volue the let ort; the let fluid node reresents the fluid volue the let ort; the leakage node reresents the fluid volue the leakage ort; the ass node reresents the u s all. Usually, the aterials for the all have good conductivity. So heat conductance of the all is neglected if the Biot nuber is less than aroxiately 0. [8]. In this study, it is assued that the Biot nuber of the coonent s all is less than 0.. he heat transfer Fig.3 Sketch a of heat transfer beteen the leakage node and the ass node is doated by convection and the heat transfer beteen ass node and the environent is doated by convection and radiation. For the fluid/all terface, the convective heat exchange Φ f is given by Φ ( ) f = kf f (6) here k f is the fluid/all heat transfer coefficient, is the heat transfer area side the all, f is the fluid teerature and is the all teerature. he heat transfer coefficient k f is defed by λnu kf = (7) l here λ is the fluid conductance, l is the secific length, Nu is Nusselt nuber hich is calculated by exerients. he functional exression for Nu deends on the resective coonent(see Ref.[9]). For the all/abient terface, the heat transferred by radiation is given by 4 4 Φrad = εσ a( a ) (8) here σ is Stefan-Boltzann constant and ε is the eissivity. For ε tyical values are taken fro Refs. [0] and []. 3 Matheatical Models For the let and let fluid nodes, the tie rate of change of the teerature can be exressed accordg to Eqs.(4) and (5). d = [ ρqil( c ( ) + ( α ( + )/ 2) c d ν ( = c )) + ρωd( c [ ( )) + α V ρωd( c ( ) + ( α ( + d (9) )/ 2) d ν ( )) + α V (20) here is the teerature the let fluid node, V is the volue the let fluid node, is the teerature the let fluid node, V is the volue the let fluid node, is the ressure the let fluid node, is the ressure the let fluid node, Q il is the ternal leakage flo rate, ω is the

4 Neveber 2006 heral-hydraulic Modelg and Siulation of Piston Pu 357 shaft rotational seed and D is the dislaceent of the u. he differential equations for the leakage node and ass node can be ritten as Eqs.(2) and (22) accordg to Eqs. (4), (5) and (6). d = [ ρqel( c ( ) + ( α ( + )/ 2) c d ν ( )) k εσ = c a ( 4 [ k f 4 a f f f ( ( ) k ) + ωd( ) + α V a a ( d )( η )/ η ) a ] (2) (22) here is the teerature the leakage node, is the teerature of the ass node, is the ressure the leakage node, a is the heat transfer area side the all, f is the heat transfer area side the all, Q el is the external leakage flo rate, η is echanical efficiency of the u and c is the secific heat of the all. Eqs.(9), (20), (2) and (22) are the basic theral equations to calculate the teerature changes each chaber of the iston u. 4 Siulation Results he siulated syste is shon Fig.4. he syste corises a iston u ith external case dra (the tye is YZB2), loadg valve, heat exchanger and reservoir. herocoules can sensor the teeratures the nodes of the u. lthough the hydraulic syste is a little sile, it is enough to test the validity of the u odel. In the exerients, the syste volue flo is changed by adjustg the load valve based on the real orkg conditions. In this study, the total test tie is 8400 s. he volue flo change of the syste is shon Fig.5. Fig. 5 Volue flo change of the syste Because it is assued that the average enthaly ith the control volue equates to the leavg enthaly, the fluid teerature leavg the volue is equal to the teerature the volue. So the teeratures of let and leakage node are easy to easure. So the test, the teerature of the let node, leakage node and the teerature flo to the u are easured. is the ut data accordg to Eq. (9). he coarisons of the test and siulation teeratures of the u s all and leakage ort are shon Fig.6 and Fig.7. his coarison yields a good agreeent beteen calculated and easured teeratures. Fig. 6 Model/rig teerature resonse of u s all Fig. 7 Model/rig teerature resonse of u s leakage ort Fig. 4 est rig for theral-hydraulic analysis of the iston u 5 Conclusions he fundaental ethod of odelg ther-

5 358 LI Cheng-gong, JIO Zong-xia CJ al-hydraulic iston u is troduced and the atheatical odel of the u is derived this aer. he theral-hydraulic odel can be alied any iston u theral-hydraulic syste calculations. For the circuit studied, the good corresondence is achieved beteen the odel and rig. hese results also validate the odellg ethods. Values of the theral-hydraulic araeters for the iston u are very iortant. So before calculatg the teerature changes of the u, the u odel and araeters ust be validated through exerients. References [] Kjølle P. Relationshi of v Conditions and c of oils for therodynaic easureents[r]. NEL Reort No 658, Noray: National Engeerg Laboratory, 978. [2] Norgard J S. herodynaic deteration of oer loss hydraulic coonents[j]. Journal of Fluids Engeerg, ransactions of SME, 973,95:2-72. [3] Dorey R E, Harris R M. eerature and its effect uon the erforance of hydraulic systes odellg and siulation[c]// Proc of the 2nd International Conference on Fluid Poer ransission and Control. Hangzhou, Cha: International cadeic Publishers, 989: [4] Storck K. heral syste analysis heat transfer glass forg and fluid teerature-control systes[d]. Lkög, Seden: Lkög University, 998. [5] Van Wylen G P, Sonntag R E. Fundaentals of classical therodynaics[m]. 3rd edition. Ne York: John Wiley & Sons, 985. [6] Sears F W, Salger G L. herodynaics, ketic theory and statistical therodynaics[m]. 3rd edition. Readg, Mass: ddison-wesley, 975. ance rediction fluid oer systes[c]//proceedgs of the Institution of Mechanical Engeers (IMechE). London: Institution of Mechanical Engeers, (4): [8] Holan J P. Heat ransfer[m]. 7th edition. Ne York: cgra-hill, 992. [9] Engelhar J. heral siulation of an aircraft fluid oer syste ith hydraulic-electrical oer conversion units[c]//proc of st FPNI-PhD Sy. 2000: [0] bshire R W. echnical considerations designg a hydraulic syste for the SS[C]//SE Conference Proceedgs. erosace Fluid Poer, 965. [] VDI-Wäreatlas. Berechnungsblätter für den Wäreübergang[M]. 7th edition. Düsseldorf: VDI Verlag, 994. Biograhy: LI Cheng-gong Born 980, he received B.S. fro Beijg University of eronautics and stronautics No he is doctor candidate Beijg University of eronautics and stronautics. el: (00) , E-ail: cario@vi. sa.co JIO Zong-xia Born 963, he received B.S. and M.S. fro Zhejiang University 985 and 988 resectively. He received his doctoral degree 99. Fro 99 to 993, he did ost-doctor research Beijg University of eronautics and stronautics and becae a teacher there. In 996, he becae a entor of doctoral students. He has ublished several scientific aers various eriodicals. el: (00) , E-ail: zxjiao@buaa.edu.cn [7] Slidders J, illey D G, Chale P J. heral-hydraulic erfor-