THE INFLUENCE OF THE ROTOR ARCHITECTURE OF A ROTATING WORKING MACHINE ON THE DRIVING POWER

Transcription

1 U.P.B. Sci. Bull., Seie D, Vol. 77, I. 1, 015 ISSN THE INFLUENCE OF THE ROTOR ARCHITECTURE OF A ROTATING WORKING MACHINE ON THE DRIVING POWER Antonio DETZORTZIS 1, Nicolae BĂRAN, Malik N. HAWAS 3 Thi pape peent a new type of otating woking machine that can be ued a a pump, fan, and blowe; in theoetical and expeimental eeach, the woking fluid i ai, it will be analyzed a a blowe, a low peue compeo. The machine i equipped with two pofiled oto that can be contuctively pefomed in two veion: I) pofiled oto with contant thickne; II) pecially manufactued oto. Fo the two veion, the powe lot by vicou fiction between the oto and the machine cae wall i calculated. In the end of the pape, the theoetical eeach ae validated by meauement pefomed on an expeimental intallation deigned and contucted in the laboatoy of the Depatment of Themodynamic, Engine, Themal and Refigeation Equipment fom Univeity Politehnica of Buchaet. Keywod: Rotating machine, pofiled oto, diving powe. 1. Intoduction The "otating machine" tem elate to the fact that the peented contuction olution can be ued a a fan, pump, low-peue compeo, and blowe. Thi pape i a contibution to the theoetical and expeimental eeach in the field of otating compeo with application to the tudy of pofiled oto. The tudy of pofiled oto achitectue i complex; it equie themodynamic, mechanic, mathematical analyi, compute pogamming notion. The pofiled oto achitectue i a figue, which, following the eeache conducted ove time, change in hape. 1 PhD. Stud., Dept. of Themotechnic, Engine, Themic and Refigeation Plant, Univeity POLITEHNICA of Buchaet, tony@elom.net Pof., Dept. of Themotechnic, Engine, Themic and Refigeation Plant, Univeity POLITEHNICA of Buchaet, Romania, n_baan_fimm@yahoo.com 3 PhD. Stud., Dept. of Themotechnic, Engine, Themic and Refigeation Plant, Univeity POLITEHNICA of Buchaet, Romania, maliknhawa@yahoo.com

2 156 Antonio Detzotzi, Nicolae Băan, Malik N. Hawa The aim i to achieve a oto hape o that the ciculated flow ate to be a high a poible and the machine diving powe a mall a poible. The pape peent two contuctive veion: I) Veion I - pofiled oto with contant thickne; II) Veion II-pecially manufactued oto. Fo each veion the calculation elation fo the flow ate and the diving powe of the machine ae peented; the powe lot by fiction between the oto and the cae i calculated. The theoetical and expeimental eeache wee conducted in the laboatoy of the Depatment of Themodynamic, Engine, Themal and Refigeation Equipment fom Univeity POLITEHNICA of Buchaet.. Machine with two pofiled oto having contant thickne.1. The contuctive olution and the opeating pinciple The machine ha two pofiled oto which otate in the oppoite diection within a cae (Fig. 1). The ynchonou otation of the oto (3, 8) i povided by two geawheel, which fom a cylindical gea with taight teeth. The gea wheel ae mounted on the haft (5) and (9) outide of the machine; duing the otational movement, the otay piton (4) ente into the cavitie of the adjacent oto. The oto pofile hape ha been etablihed in [1,] and the manufactuing technology in [3,4]. With the notation fom Fig. 1, the flow ate and the diving powe of the machine calculation elation ae [5,6,7]: n 3 V = πlz( + z) [ m / ] (1) 30 n Pm = VmΔ p= π l z ( + z) Δp [ W ] () 30 whee n -the machine otation, Δp- the inceae in peue between uction and dichage [N/m ].

3 The influence of the oto achitectue of a otating woking machine on the diving powe c 5 z a Φ l a b Fig. 1. Co ection (a) and longitudinal ection (b) though the blowe 1-ga uction connection; -uppe cae; 3-uppe oto; 4- otating piton; 5-diven haft; 6-cavity; 7-ga dichage connection; 8-lowe oto; 9-diving haft; 10-contact uface between the oto and the cae wall; 11-uppot a - haft adiu; - oto adiu; z- piton height.. The detemination of lot powe though vicou fiction between the oto and the ide wall of the cae (Veion I) Calculation hypothee: - The fiction between the top of the piton and the cae i neglected. - The font uface of the piton complete the cavitie ceated in the oto, o the calculation aea i fom a to (fig. 1). -The fluid velocity at each point on the font uface of the oto i equal to the oto velocity. - The velocity at a point on the uface of the dik will be in the ange of: wa = ω a and w = ω [ m/ ] (3) It i equied to etablih the conumed powe though vicou fiction between the font uface of the oto and the cae wall.

4 158 Antonio Detzotzi, Nicolae Băan, Malik N. Hawa A initial data ae known: - The haft adiu on which the oto i mounted: = a m; the oto exteio adiu: = m; -The angula velocity fo a given pm of the dik; - The dynamic vicoity of ai at t = 0 C i found fom [8,9]: 6 N ηai = m -The gap between the dik and the cae wall i choen equal to the CNC peciion poceing [10]: = m. The calculation i made fo one oto. Fom mechanic i known that the toque i the poduct between the foce and the foce am. The elementay eitant toque due to vicou fiction between the oto and the two wall of the cae will be [11]: dm = dff (4) whee F f i the vico fiction foce. dff =τ da (5) τ- tangential effot; da elementay uface aea (Fig.). τ da= π d τ Fig.. Plan view of a potion of the oto da = π d (6) The tangential tenion (hea te) due to fluid vicoity i calculated with Newton fomula [1,13]: τ = η dw (7) dy whee the coodinate y i meaued pependiculaly to the dik uface (Fig. 3).

5 The influence of the oto achitectue of a otating woking machine on the diving powe 159 Fig. 3. Computing ection 1- cae; - thin laye of fluid; 3- oto dik; 4-haft The velocity gadient fo the bounday laye with "" thickne, auming a linea vaiation, ha the expeion: dw ω = (8) dy Equation (8) become: ω τ = η (9) Equation (5), taking into account equation (6) and (9) become: ω ω df = η πd = π η d (10) A moe exactly calculation can be pefomed uing the dynamic bounday laye theoy [14,15]. Fom equation (4) and (10) i obtained: ω dm = π η d (11) M 3 4 π ω η = dm d (1) 0 a π η ω 4 4 M = [ a ] [ N m] (13) Fom mechanic i known the elation of conumed powe computing to ovecome the vicou fiction fo one oto [11]: P1 = M ω [ W ] (14) Fo the entie machine, the conumed powe by vicou fiction (P m ) will be: Pm = P1 [ W ] (15) Intoducing the elation (13) and (14) into (15) it eult:

6 160 Antonio Detzotzi, Nicolae Băan, Malik N. Hawa π η ω 4 4 Pm = ( a ) (16) Fom equation (16) i obeved that fo a given contuctive olution the value of P m i influenced by η and ω. In what follow, the influence of the oto achitectue (veion I and veion II) function of ω, the value of η emaining contant, i tudied. I calculated the powe lot by vicou fiction between the fontal uface of the oto and the cae wall with the value of η fo ai and ω given by n = 00, 400, 600, 800, 1000 pm. π n π ω 1 = = 00 = 0.93 ad / (17) ( 0.93) 3 3 P 3 ( ) ( 9 10 ) m = = W (18) Similaly the calculation ae made fo othe value of n eulting the data in Table 1. Table 1 Value of P m =f(n ) fo veion I n [ot/min] ω [ad/] P m [W] Baed on the data in Table 1, the cuve P m = f (n ) i plotted (Fig. 4). Fig. 4. P m = f (n ) fo ai, veion I Fom Fig.4 it i found that with the machine pm inceae, the powe conumed by vicou fiction between the machine oto and the cae the will inceae; the neceay diving powe of the machine will inceae.

7 a The influence of the oto achitectue of a otating woking machine on the diving powe Machine with two pecially pofiled oto 3.1. The contuctive olution and the opeating pinciple z 3 z c a c Fig. 5. Co ection (a) and longitudinal ection (b) though the otating blowe 1-ga uction connection; -uppe cae; 3-uppe oto; 4- otating piton; 5-diven haft; 6-cavity; 7-ga dichage connection; 8-lowe oto; 9-diving haft; 10-contact uface between the oto and the cae wall; 11-uppot In ode to bette undetand the contuctive olution in veion II, thee ha been made a photo of the cae without the cove (Fig. 6). Fig.6. Specially pofiled oto mounted in the cae

8 16 Antonio Detzotzi, Nicolae Băan, Malik N. Hawa Fom Fig. 6 one obeve that not all the lateal uface of the oto come in contact with the ide wall of the cae. The opeating pinciple of the machine i the ame a that decibed in ection Detemination of the lot powe though vicou fiction between the oto and the ide wall of the cae (Veion II) Similaly a in Paagaph.. the powe conumed by fiction between the two oto and the ide wall of the cae i: π η ω 4 4 P m = i [ N / m] (19) whee i i the inne adiu of the oto; i = 45 mm; ( 0.939) 3 3 P 3 ( ) ( ) m = = W (0) Similaly, the calculation fo n = ot/min 400, 600, 800, 1000, ae made, eulting the data in Table. Table Value of P m =f(n ) fo veion II n [ot/min] ω [ad/] P m [W] Baed on the eult in Table, the cuve P m = f (n ) i plotted in Fig. 7. Fig.7. P m = f (n ) fo ai (veion II) If gaph fom Fig. 4 and fom Fig. 7 ae ovelapped on the ame downing one obtain Fig. 8:

9 The influence of the oto achitectue of a otating woking machine on the diving powe Fig. 8. P m = f (n ) fo ai 1- P m = f (n ) veion I; - P m = f (n ) veion II; Figue 8 how that with the machine pm inceae, the powe conumed by vicou fiction between the machine oto and the cae the will inceae; the machine contuctive olution in veion II will be moe advantageou becaue the powe conumed to defeat the vicou fiction i lowe. 4. Expeimental eeache 4.1. Expeimental tand deciption The tand wa deigned o that the pefomed meauement olve the following poblem: a) - The influence of oto hape on the diving powe; b)-the contuction though expeiment of the imple chaacteitic of the machine: V = f( n); P = f( n); η = f( n ). To the tand achievement pecialty pape wee conulted [16, 17, 18]. Fom the tand cheme (Fig. 9) it follow that the main paamete: the flow (peue, tempeatue), the abobed powe and the blowe pm can be meaued.

10 164 Antonio Detzotzi, Nicolae Băan, Malik N. Hawa Fig.9. The expeimental intallation cheme fo teting a otating blowe with pofiled oto 1 ai filte; -device fo meauing the peue at the blowe uction; 3- ai tempeatue meauing device; 4-otating blowe; 5-electic moto; 6-panel with electical appliance; 7- compeed ai tank; 8-manomete with digital diplay; 9-themomete with digital diplay; 10-diffeential manomete; 11- diaphagm; 1- contol; 13 DN 50 ai dichage valve. The tand i contucted in open cicuit; it allow the meauement of the peue and ai tempeatue both on uction and dichage fom the otating blowe with pofiled oto. Fig. 10 peent a geneal view of the tand. Fig.10. Oveview of the expeimental intallation 1 electic moto; - otating blowe; 3-panel with electical appliance; 4- compeed ai tank; 5-diaphagm fo ai flow meauement 4.. Reeache methodology and obtained eult - Afte opeating the otating blowe, the contol valve (1) i fully open, thee i no hydaulic eitance at dichage. - Theeafte, though the ALTIVAR (6) device [19,0] the pm of the electic moto (5) i adjuted to the value 00, 400, 600, 800, 1000 ot/ min.

11 The influence of the oto achitectue of a otating woking machine on the diving powe 165 Simultaneouly, the powe conumed by the electic moto, that i, the powe at backlah ", i ead. - The eult of the expeimentally meaued magnitude ae hown in Table 3. Table 3 The expeimental obtained eult n [ot/min] ω [ad/] Pm [W] Va. I Va. II The powe (P m ) conumed by the machine i ued to ovecome the vicou fiction between the oto and the cae wall and to ovecome the mechanical fiction occuing in the electic moto and blowe beaing. The value of the powe abobed by the machine ae highe than the theoetical one due to the intenal and mechanical efficiency that have educed thee value. 5. Concluion Fom the theoetical and the expeimental eeache it eult: 1 - Fo a given machine contuctive olution, the powe (P m ) lot by vicou fiction between the oto and the ide wall of the cae, depend on η and ω. - When the fluid vicoity inceae, ai, wate, oil, the value of P m will inceae. 3 - When the machine pm inceae, the value of P m will inceae. 4 - The pofiled oto hape influence the powe lot by vicou fiction; theefoe, the diving powe of the machine i influenced. R E F E R E N C E S [1]. A. Cotache, N. Băan, Computation method fo etablihing the contou of a new type of pofiled oto, Univeity Politehnica of Buchaet, Scientific Bulletin, Seie D: Mechanical Engineeing, vol. 70, no.3, 008, pp []. N. Băan, A. Motoga, A. Cotache, Computing element egading the achitectue of a pofiled oto, (in Romanian), Temotehnica, Agi Publihing Houe, Buchaet, no.1, 008, pp [3]. N. Băan, D. Benea, T. Sima, A. Detzotzi, C. Cănau, Manufactuing Technology fo a New Type of Pofiled Roto, Advanced Mateial Reeach, Tan Tech Publication, Switzeland, vol , 013, pp ,. [4]. N. Băan, O. Donţu, D. Benea, A. Cotache, Contuctive element and technological pocedue ued in the contuction of a new type of otating compeo, Rev. Fine Mechanic, Optic & Mechatonic, no. 5, 004, pp

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