Investigation of the Centrifugal Force Effect to a Revolving Vane (RV) Machine

Transcription

1 Pudue Univesity Pudue e-pubs Intenational Compesso Engineeing Confeene Shool of Mehanial Engineeing 01 Investigation of the Centifugal oe Effet to a Revolving Vane (RV) Mahine Alison Subiantoo alis0004@ntu.edu.sg Kim Tiow Ooi ollow this and additional woks at: Subiantoo, Alison and Ooi, Kim Tiow, "Investigation of the Centifugal oe Effet to a Revolving Vane (RV) Mahine" (01). Intenational Compesso Engineeing Confeene. Pape This doument has been made available though Pudue e-pubs, a sevie of the Pudue Univesity Libaies. Please ontat epubs@pudue.edu fo additional infomation. Complete poeedings may be aquied in pint and on CD-ROM dietly fom the Ray W. Heik Laboatoies at Heik/Events/odelit.html

2 1111, Page 1 t Investigation of the Centifugal oe Effet to a Revolving Vane (RV) Expande Alison SUBIANTORO 1 *, Kim Tiow Ooi 1 Nanyang Tehnologial Univesity, Enegy Reseah Singapoe Phone: , fax: , alison@ntu.edu.sg Nanyang Tehnologial Univesity, Shool of Mehanial and Aeospae Engineeing Singapoe Phone: , fax: , mktooi@ntu.edu.sg * Coesponding Autho ABSTRACT The Revolving Vane (RV) mahine is unique beause the ylinde otates togethe with the oto at thei espetive axis. This auses vaious unique behavios that ae not peviously obseved in the onventional otay mahines. In this pape, the effets of the entifugal foe to the behavio of the mahine ae investigated. It is found that the entifugal foe affets the aveage output toque though the shaft beaing load and fition loss. Inteestingly, if the ente of mass is set popely, the entifugal foe an help to offset the pessue foe ating at the shaft. This helps to edue the beaing load and ineases the mehanial effiieny of the mahine. The finding an be used to optimize the RV mahine design. 1. INTRODUCTION Due to the eent demand of moe enegy effiient efigeation systems, expandes have been intensively eseahed in the past few yeas in plae of the onventional expansion valve. Simply speaking, an expande is a ompesso that opeates in the evesed yle. It takes in high pessue fluid and expands it to podue powe. The geneated powe an then be used to help to un the ompesso. At the same time, the slow expansion poess edues the thottling loss by making the poess lose to the isentopi line, ineasing the ooling apaity. One of the fist poposed appliations of expandes is fo tansitial abon dioxide efigeation systems whee due to the lage pessue diffeene used, the thottling loss is signifiantly lage. The ealy studies indiate that an expande with a 60% isentopi effiieny an inease the oeffiient of pefomane (COP) of the CO system by aound 0% (Robinson and Goll, 1998). Sine then, vaious types of expandes have been developed and studied based on the existing ompesso mehanisms. These inlude, among othes, eipoating (Baek et al., 005a, b), soll (Kim et al., 008), sew (Kovaevi et al., 006), olling piston (Matsui et al., 009) and otay vane (ukuta et al., 009). Moe eently, a new type of otay mehanism, alled the Revolving Vane (RV) mehanism, whee the ylinde otates togethe with the oto was intodued (Teh and Ooi, 006). This unique featue allows the mehanism to have less elative veloities at the ubbing sufaes, esulting in smalle fition losses. The mehanism has then been impoved by attahing the vane igidly to the oto (Teh and Ooi, 008b) and also used fo expande appliations (Subiantoo and Ooi, 009). An illustation of the woking poess of the RV expande is shown in igue 1. Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01

3 1111, Page igue 1: Woking poess of the RV expande Vaious aspets of the mehanism have been studied, these inlude the fition losses (Subiantoo and Ooi, 011; Teh and Ooi, 008b), intenal leakages (Teh and Ooi, 008a) and vane aangement (Subiantoo and Ooi, 010). In this pape, the effets of the entifugal foes of the omponents ae analyzed. The analysis will be foused on the effet to the expande toque podution.. THEORETICAL MODEL The study is aied out mathematially. o simplifiation, the following assumptions ae made: Adiabati poess is assumed fo all poesses. Pefetly sealed model is assumed. The diving shaft opeates at a onstant angula veloity. The fitional losses only ou at the shaft beaings, vane side and endfaes, sine othe fitional losses ae negligible. The mathematial models inlude the themodynamis, kinematis and dynamis aspets of the expande. They ae solved with the Runge-Kutta method using a ompute ode witten in the otan pogamming language. The themodynamis model, whih simulates the themodynamis of the woking fluids in the two woking hambes, is solved fist based on equation (1), whih is the enegy balane equation. The esults ae then used to simulate the dynamis aspets based on equations ()-(7). They ae deived fom the fee body diagams of the oto and the ylinde. Detailed pesentations of the deivations an be found elsewhee (Subiantoo and Ooi, 009). They inlude the alulations of the expande output toque, T gen, the vane ontat foe, v,n, and the shaft beaings loads, b. Centifugal foes ou at both the oto and the ylinde and affet the pefomane of the expande though the shaft beaing loads. du v dmv dqv dwv v i dm + = + i v o dmo mv uv hi + ho + (1) dt dt dt dt i dt o dt l ve dl ve dt wv T = gen v, p v, n + lve η v T () dlve dt I α T v, n = (3) v, n dlve dt os v, n wv sin γ ηv γ dl v, n ve dt v, n Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01

4 1111, Page 3 ϕ b, x, = v, n os ϕ + v, f sinϕ p, sin t, sin( ϕ + θt, ) + loss, x, (4) ϕ b, y, = v, n sin ϕ + v, f osϕ p, os t, os( ϕ + θt, ) + loss, y, (5) ϕ b, x, = v, p os ϕ + v, n osϕ v, f sinϕ + p, sin t, sin( ϕ + θ t, ) + loss, x, (6) ϕ b, y, = v, p sin ϕ v, n sinϕ v, f osϕ + p, os t, os( ϕ + θt, ) + loss, y, (7) whee: = m ω t, t, t, = m t, ω = ( psv pdv ) l exp sin( ϕ / ) ( psv pdv ) lexp sin( ϕ / ) ( psv pdv ) lve exp p, = p, v, p = l The definitions of the angle and the adius of the ente of mass, θ t and t, ae shown in igue. ente of mass of ylinde ente of mass of oto t, C θ t, t, R θ t, ϕ ϕ igue : Shemati diagams of the ylinde and the oto The main dimensions and paametes of the simulated expande model ae listed in Table 1. Table 1: Main dimensions and paametes of the expande model Radius of oto body 9 mm + Inne adius of ylinde body Length of expande Diamete of oto shaft beaing Length of oto uppe shaft beaing Length of oto lowe shaft beaing 35 mm 5 mm 5 mm 40 mm 0 mm Radial leaane of oto shaft beaings 15 µm Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01

5 1111, Page 4 Diamete of ylinde shaft beaing Length of ylinde shaft beaings 49. mm 10 mm Radial leaane of ylinde shaft beaings 30 µm Rotating inetia of oto 0.1 g.m Rotating inetia of ylinde.81 g.m ition oeffiient of vane 0.15 Dishage oeffiient of pots 0.7 Lubiant visosity Diamete of sution pots (3 numbes) Diamete of dishage pots (3 numbes) Pa.s 6.4 mm 4.6 mm Cylinde endfae total gap width 100 µm Mass of oto Mass of ylinde Distane of ente of oto mass fom oto ente Distane of ente of ylinde mass fom ylinde ente kg kg 9 mm 35 mm 3. RESULTS AND DISCUSSIONS To assist in the obsevation of the effets of the entifugal foes to the expande pefomane, a non-dimensional paamete alled the Toque Diffeene, abbeviated as TD, is intodued. The definition is as shown in equation (8). T sim is the output toque obtained fom the simulation of the expande with the onsideation of the entifugal foe(s). T 0 is the benhmak toque, whih is equal to 0.78 Nm and is the output toque of the expande without any entifugal foe. TD Tsim T0 = (8) T 0 The effet of the dietion of the entifugal foe is shown in igue 3 though the elationship between TD and the angle of the entes of both the ylinde and the oto masses. It an be seen that the entifugal foes of the omponents an deease the expande pefomane signifiantly. This is beause the entifugal foes add moe loads to the shaft beaings, esulting in moe losses at the beaings. The wost onfiguations ae when the angles of Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01

6 1111, Page 5 the ylinde and the oto entes of mass ae at 0 and 180, with TD values of aound -8% and -8%, espetively. Duing the design stage, it is impotant to ensue that the entes of mass do not lie in the viinities of these values. The entifugal foe of the ylinde is moe signifiant in affeting the expande pefomane beause the ylinde has moe mass and is lage in size as ompaed to the oto. igue 3: Relationship between TD and the angle of ente of mass Inteestingly, igue 3 also indiates that the entifugal foes, espeially those at the ylinde, an impove the expande pefomane by %. The best onfiguation is when the angle of the ylinde is aound 135. The impovement aused by the oto entifugal foe is insignifiant, less than 0.%. To undestand the eason behind this behavio, the ompaison of the pofiles of the output toque when the expande expeienes no entifugal foe and when it expeienes a entifugal foe at the ylinde with the angle of ente of ylinde mass equals to 135 is shown in igue 4. igue 4: Compaison of output toque pofiles of the expande with no entifugal foe and with the ylinde entifugal foe at an angle of ylinde mass of 135 igue 4 shows that when thee is a entifugal foe at the ylinde whee the ylinde mass is loated at an angle of 135, the amplitude of the expande output toque pofile beomes lage than that of the expande with no entifugal foe. The negative peak is moe negative beause the entifugal foe adds moe load the shaft beaing, Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01

7 1111, Page 6 esulting in moe beaing fition loss. The positive peak is highe is highe in value beause the entifugal foe helps to edue the pessue load, esulting in less fition loss in the viinity. This is illustated in igue 5. Beause the pessue diffeene aoss the vane is at its highest hee, this impovement is moe signifiant than the deline of the negative peak, esulting in the oveall expande pefomane. θ t, t, p, ϕ t, igue 5: Inteation between entifugal foe and pessue load igue 5 shows the situation when the ylinde angle, ϕ, is aound 135 and the angle of the ente of the ylinde mass is designed as 135. The pessue load at the ylinde is epesented by p, and is ating in the dietion towads the lowe left hand one of the diagam. On the othe hand, the entifugal foe, t,, is ating in the opposite dietion towads the uppe ight hand one. Hene, the esultant foe ating on the ylinde shaft is smalle than p,. This auses the beaing load and its fition loss to deease. The effet of the magnitude of the entifugal foe of the ylinde to expande pefomane is shown in igue 6. The magnitude is vaied by vaying the distane between the ente of the ylinde mass and the ylinde ente fom 5 mm to 50 mm. It an be seen that thee is an optimum distane, aound 35 mm. Howeve, the hange in TD is small, less than 0.%. igue 6: Relationship between TD and the distane of ente of ylinde mass fom ylinde ente Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01

8 1111, Page 7 4. CONCLUSION In this pape, the effets of entifugal foe to the Revolving Vane expande pefomane have been studied. The pefomane indiato is the aveage output toque of the expande. om the study, the following findings ae obseved: 1. The entifugal foe of the ylinde affets the pefomane moe signifiantly than the oto beause the ylinde has moe mass and is lage in size, esulting in a lage entifugal foe.. The output toque of the expande an dop by as muh as 8%. This happens if the ente of mass of the ylinde is loated nea the line onneting the ylinde ente and the vane slot (angle of ente of ente of ylinde mass of 0 ). 3. om ou study, the entifugal foe of the ylinde an impove the expande pefomane by about % if the ente of the ylinde mass is loated an angle of aound 135. The eason behind the impovement is beause the entifugal foe edues the beaing load when the pessue load is highest. 4. By vaying the distane between the ylinde mass and the ylinde ente, whih esults in the hange of the entifugal foe magnitude, it an be obseved that the optimum distane is at aound 35 mm. Howeve, the oveall vaiation in the output toque is less than 0.%. NOMENCLATURE foe (N) Subsipts I otating inetia (kg.m ) b beaing l length (m) ylinde m mass (kg) t entifugal p pessue (Pa) v ontol volume P powe (W) dv dis. hambe Q heat enegy (J) exp expande adius (m) f fition t time (s) gen geneated T toque (Nm) i inlet u intenal enegy (J/kg.K) n nomal v veloity (m/s) o outlet w width (m) p pessue W wok (J) oto α angula aeleation (ad/s ) sv sut. hambe γ angle between oto and v vane ylinde adii at vane ontat (ad) ve exposed vane ϕ angle (ad) x x-axis dietion η fition oeffiient (-) y y-axis dietion θ angle (ad) ω angula speed (ad/s) REERENCES Baek, J.S., Goll, E.A., Lawless, P.B., 005a. Piston-ylinde wok poduing expansion devie in a tansitial abon dioxide yle. Pat I: expeimental investigation. Intenational Jounal of Refigeation, vol. 8, no. : p Baek, J.S., Goll, E.A., Lawless, P.B., 005b. Piston-ylinde wok poduing expansion devie in a tansitial abon dioxide yle. Pat II: theoetial model. Intenational Jounal of Refigeation, vol. 8, no. : p ukuta, M., Yanagisawa, T., Higashiyama, M., Ogi, Y., 009. Pefomane of vane-type CO expande and haateistis of tansitial expansion poess. HVAC and R Reseah, vol. 15, no. 4: p Kim, H.J., Ahn, J.M., Cho, S.O., Cho, K.R., 008. Numeial simulation on soll expande-ompesso unit fo CO tans-itial yles. Applied Themal Engineeing, vol. 8, no. 13: p Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01

9 1111, Page 8 Kovaevi, A., Stosi, N., Smith, I.K., 006. Numeial simulation of ombined sew ompesso-expande mahines fo use in high pessue efigeation systems. Simulation Modelling Patie and Theoy, vol. 14, no. 8: p Matsui, M., Hasegawa, H., Ogata, T., Wada, M., 009. Development of the high-effiieny tehnology of a CO two-stage otay expande. HVAC and R Reseah, vol. 15, no. 4: p Robinson, D.M., Goll, E.A., Effiienies of tansitial CO yles with and without an expansion tubine. Intenational Jounal of Refigeation, vol. 1, no. 7: p Subiantoo, A., Ooi, K.T., 009. Intodution of the evolving vane expande. HVAC and R Reseah, vol. 15, no. 4: p Subiantoo, A., Ooi, K.T., 010. Design analysis of the novel Revolving Vane expande in a tansitial abon dioxide efigeation system. Intenational Jounal of Refigeation, vol. 33, no. 4: p Subiantoo, A., Ooi, K.T., 011. Analytial study of the endfae fition of the evolving vane mehanism. Intenational Jounal of Refigeation, vol. 34, no. 5: p Teh, Y.L., Ooi, K.T., 006. Design and fition analysis of the evolving vane ompesso, Intenational Compesso Engineeing Confeene at Pudue, p. C046. Teh, Y.L., Ooi, K.T., 008a. Analysis of intenal leakage aoss adial leaane in the impoved evolving vane (RV-i) ompesso, Intenational Compesso Engineeing Confeene at Pudue, p Teh, Y.L., Ooi, K.T., 008b. Design and fition analysis of the impoved evolving vane (RV-i) ompesso, Intenational Compesso Engineeing Confeene at Pudue, p Intenational Compesso Engineeing Confeene at Pudue, July 16-19, 01